How Is Comparing Decimals Similar to Comparing Whole Numbers?

Comparing decimals and whole numbers might seem different, but the underlying principle is the same: understanding place value. At COMPARE.EDU.VN, we break down this process to show you the similarities and how to easily compare any numbers. Discover how understanding place value helps in comparing and determining the value of numbers, enhancing your numerical skills.

1. What’s the Connection Between Decimals and Whole Numbers in Comparisons?

Comparing decimals shares a fundamental similarity with comparing whole numbers: both rely on the principle of place value. In whole numbers, each digit’s position represents a power of ten (ones, tens, hundreds, etc.). Similarly, decimals extend this concept to the right of the decimal point, representing fractions of ten (tenths, hundredths, thousandths, etc.). When comparing numbers, whether whole or decimal, we start by examining the digits with the highest place value and proceed to the right until a difference is found. This systematic approach allows us to determine which number is larger or smaller.

To illustrate this, consider comparing the whole numbers 1,234 and 1,567. We begin by comparing the thousands place (1 in both numbers). Since they are equal, we move to the hundreds place, where 5 is greater than 2. Therefore, 1,567 is larger than 1,234.

Now, let’s compare the decimals 0.64 and 0.362. We start by comparing the tenths place. Here, 6 is greater than 3, so 0.64 is larger than 0.362. Notice how the process mirrors that of whole numbers. Understanding place value is key to both. This method ensures accuracy and efficiency in determining the relative size of numbers. Use COMPARE.EDU.VN to easily compare decimals and whole numbers with our detailed guides and examples.

2. Breaking Down the Place Value System for Decimals and Whole Numbers

The place value system is the backbone of numerical comparison, and understanding it is crucial for both decimals and whole numbers. In whole numbers, each digit’s position determines its value:

Ones: The rightmost digit represents single units.
Tens: The next digit to the left represents groups of ten.
Hundreds: The next digit represents groups of one hundred, and so on.

For example, in the number 3,785:

5 is in the ones place, representing 5 x 1 = 5
8 is in the tens place, representing 8 x 10 = 80
7 is in the hundreds place, representing 7 x 100 = 700
3 is in the thousands place, representing 3 x 1000 = 3000

Decimals extend this system to the right of the decimal point, representing fractions of one:

Tenths: The first digit to the right of the decimal point represents tenths (1/10).
Hundredths: The second digit represents hundredths (1/100).
Thousandths: The third digit represents thousandths (1/1000), and so on.

For example, in the decimal 0.459:

4 is in the tenths place, representing 4/10 = 0.4
5 is in the hundredths place, representing 5/100 = 0.05
9 is in the thousandths place, representing 9/1000 = 0.009

When comparing numbers, we align them based on their place values. For whole numbers, this means aligning the ones place. For decimals, we align the decimal points. For instance, to compare 123.45 and 87.6, we align the decimal points:

  123.45
   87.60  (We can add a zero to 87.6 to align the hundredths place)

Starting from the leftmost digit (the hundreds place), we compare the digits in each place value. If they are equal, we move to the next place value to the right until we find a difference. This systematic approach, grounded in understanding place value, ensures accurate comparison of both decimals and whole numbers. For more detailed explanations and examples, visit COMPARE.EDU.VN, where we simplify complex numerical concepts.

3. Step-by-Step Guide to Comparing Decimals Like Whole Numbers

To effectively compare decimals, follow these steps, which mirror the process used for whole numbers:

Step 1: Align the Decimal Points:
Write the numbers vertically, aligning the decimal points. This ensures that digits with the same place value are in the same column. For example, to compare 45.67 and 45.8, align them as follows:
```
45.67
45.80 (Add a zero to make the number of decimal places the same)
```
Step 2: Compare the Whole Number Parts:
Start by comparing the digits to the left of the decimal point. If these digits are different, the number with the larger whole number part is the greater number. In the example above, both numbers have 45 as the whole number part, so we move to the next step.
Step 3: Compare the Decimal Parts:
Begin comparing the digits to the right of the decimal point, starting with the tenths place. If the digits in the tenths place are different, the number with the larger digit is the greater number. In our example, we compare 6 (in 45.67) and 8 (in 45.80). Since 8 is greater than 6, 45.80 is greater than 45.67.
Step 4: Continue Comparing if Necessary:
If the digits in the tenths place are the same, move to the hundredths place, then the thousandths place, and so on, until you find a place value where the digits differ. The number with the larger digit in that place value is the greater number.
Step 5: Add Zeros as Placeholders:
If one number has fewer decimal places than the other, add zeros to the end of the shorter number so that both numbers have the same number of decimal places. This does not change the value of the number but makes the comparison easier. For instance, if comparing 3.4 and 3.456, rewrite 3.4 as 3.400.
Example: Compare 12.345 and 12.341
- Align the decimal points:
```
12.345
12.341
```
- The whole number parts are the same (12).
- The tenths and hundredths places are the same (3 and 4).
- In the thousandths place, 5 is greater than 1.
- Therefore, 12.345 > 12.341.

By following these steps, you can confidently compare decimals, just as you would compare whole numbers. Visit COMPARE.EDU.VN for more resources and practice exercises to master decimal comparison.

4. The Role of Zero: Placeholder and Value Determiner in Decimal Comparisons

Zero plays a critical role in comparing decimals, serving both as a placeholder and a value determiner. Understanding these functions is essential for accurate comparisons.

Zero as a Placeholder:
Adding zeros to the right of the last digit after the decimal point does not change the value of the decimal but helps in aligning the numbers for comparison. For example, 0.5 is the same as 0.50 or 0.500. Adding these zeros makes it easier to compare 0.5 with decimals like 0.52 or 0.515.

Consider comparing 0.7 and 0.78. By adding a zero to 0.7, we rewrite it as 0.70. Now, it’s easier to see that 0.78 is greater than 0.70 because 78 hundredths is more than 70 hundredths.
Zero as a Value Determiner:
Zeros within a decimal number can significantly affect its value. For instance, 0.05 is different from 0.5. In 0.05, the zero in the tenths place indicates that there are no tenths, making the value smaller than 0.5, where there are five tenths.

When comparing decimals, it is crucial to consider the placement of zeros. For example, comparing 0.03 and 0.3:
- 1. 03 has zero tenths and three hundredths.
- 1. 3 has three tenths and zero hundredths.
Since three tenths (0.3) is greater than zero tenths and three hundredths (0.03), 0.3 is the larger number.
Examples Illustrating the Role of Zero:
- Example 1: Compare 0.6 and 0.602
  - Rewrite 0.6 as 0.600 for easier comparison.
  - Comparing 0.600 and 0.602, we see that the tenths and hundredths places are the same.
  - In the thousandths place, 0.600 has 0, while 0.602 has 2.
  - Therefore, 0.602 is greater than 0.6.
- Example 2: Compare 0.08 and 0.8
  - 1. 08 has zero tenths and eight hundredths.
  - 1. 8 has eight tenths and zero hundredths.
  - Clearly, 0.8 is greater than 0.08.

Understanding the role of zero in decimals ensures accurate comparisons and prevents common errors. For more insights and practical exercises, visit COMPARE.EDU.VN, where we provide comprehensive resources for mastering decimal concepts.

5. Converting Fractions to Decimals for Easier Comparison

When comparing fractions and decimals, converting the fraction to a decimal is often the easiest way to facilitate the comparison. This process involves dividing the numerator of the fraction by its denominator. Once the fraction is in decimal form, you can compare it directly with other decimals using the methods discussed earlier.

Converting Fractions to Decimals:
To convert a fraction to a decimal, perform the division. For example, to convert 3/4 to a decimal, divide 3 by 4:
```
3 ÷ 4 = 0.75
```
So, the fraction 3/4 is equal to the decimal 0.75.
Examples of Fraction-to-Decimal Conversions:
- Example 1: Convert 1/2 to a decimal.
```
1 ÷ 2 = 0.5
```
  Therefore, 1/2 = 0.5.
- Example 2: Convert 5/8 to a decimal.
```
5 ÷ 8 = 0.625
```
  Therefore, 5/8 = 0.625.
- Example 3: Convert 7/20 to a decimal.
```
7 ÷ 20 = 0.35
```
  Therefore, 7/20 = 0.35.
Comparing Fractions and Decimals:
Once the fraction is converted to a decimal, you can easily compare it with other decimals. For example, compare 3/4 and 0.8:
- Convert 3/4 to 0.75.
- Now compare 0.75 and 0.8.
- Since 0.8 is greater than 0.75, 0.8 is greater than 3/4.
Step-by-Step Example:
Compare 2/5 and 0.35.
- Convert 2/5 to a decimal: 2 ÷ 5 = 0.4
- Now compare 0.4 and 0.35.
- Rewrite 0.4 as 0.40 for easier comparison.
- Since 0.40 is greater than 0.35, 2/5 is greater than 0.35.
Handling Repeating Decimals:
Some fractions, when converted to decimals, result in repeating decimals (e.g., 1/3 = 0.333…). In such cases, you can either round the decimal to a certain number of places or compare the repeating decimal by considering enough digits to make an accurate comparison. For instance, when comparing 1/3 and 0.34:
- 1/3 = 0.333…
- Comparing 0.333… and 0.34, we can see that 0.34 is greater because it has 4 in the hundredths place, while 0.333… has only 3.

Converting fractions to decimals simplifies the comparison process, allowing you to apply the same techniques used for comparing whole numbers and decimals directly. For more detailed explanations and examples, visit COMPARE.EDU.VN, where we offer a variety of tools and resources for mastering numerical comparisons.

6. Visual Aids: Using Number Lines to Compare Decimals

Number lines are powerful visual tools for comparing decimals. They provide a clear representation of the relative positions of numbers, making it easier to understand their values and compare them.

How to Use a Number Line:
To compare decimals on a number line, follow these steps:
- Draw the Number Line: Draw a straight line and mark the endpoints with appropriate whole numbers that include the decimals you want to compare. For example, if you are comparing 2.3 and 2.7, you can mark the endpoints as 2 and 3.
- Divide the Line: Divide the space between the whole numbers into tenths. Each division represents 0.1. Mark these divisions clearly.
- Plot the Decimals: Locate and mark the decimals on the number line. For example, 2.3 would be three divisions to the right of 2, and 2.7 would be seven divisions to the right of 2.
- Compare the Positions: The decimal that is farther to the right on the number line is the greater number. In this case, 2.7 is to the right of 2.3, so 2.7 > 2.3.
Examples of Comparing Decimals on a Number Line:
- Example 1: Compare 0.4 and 0.6
  - Draw a number line from 0 to 1.
  - Divide the line into tenths.
  - Mark 0.4 and 0.6 on the line.
  - Since 0.6 is to the right of 0.4, 0.6 > 0.4.
- Example 2: Compare 1.2 and 1.5
  - Draw a number line from 1 to 2.
  - Divide the line into tenths.
  - Mark 1.2 and 1.5 on the line.
  - Since 1.5 is to the right of 1.2, 1.5 > 1.2.
- Example 3: Compare 2.15 and 2.3
  - Draw a number line from 2 to 3.
  - Divide the line into tenths.
  - Estimate the position of 2.15 (slightly to the right of 2.1) and mark 2.3.
  - Since 2.3 is to the right of 2.15, 2.3 > 2.15.
Benefits of Using Number Lines:
- Visual Clarity: Number lines provide a visual representation that makes it easier to understand the relative values of decimals.
- Intuitive Comparison: Seeing the positions of numbers on a line helps in quickly determining which number is greater.
- Educational Tool: Number lines are excellent for teaching and learning decimal concepts, especially for those who benefit from visual aids.

Using number lines is an effective way to enhance your understanding of decimal comparisons. For more visual aids and interactive tools, visit COMPARE.EDU.VN, where we provide resources to help you master numerical concepts.

7. Common Mistakes to Avoid When Comparing Decimals

When comparing decimals, several common mistakes can lead to incorrect conclusions. Being aware of these pitfalls can help you avoid them and ensure accurate comparisons.

Ignoring Place Value:
One of the most common mistakes is failing to properly consider place value. For example, assuming that 0.9 is smaller than 0.12 because 9 is less than 12. This is incorrect because 0.9 represents nine tenths, while 0.12 represents twelve hundredths. To compare correctly, rewrite 0.9 as 0.90 and then compare 0.90 and 0.12. It’s clear that 0.90 > 0.12.
Adding Zeros Incorrectly:
Adding zeros to the left of a decimal or within a decimal number (other than as a placeholder to the right of the last digit) changes its value. For example, changing 0.5 to 0.05 makes the number smaller (five hundredths instead of five tenths). Adding zeros to the right, like changing 0.5 to 0.50 or 0.500, is valid because it doesn’t change the value.
Comparing Unequal Decimal Places Without Alignment:
When comparing decimals with different numbers of decimal places, it’s important to align the decimal points and add zeros as placeholders. For example, to compare 4.5 and 4.567, align them as:
```
4.  500
5.  567
```
Now it’s easier to see that 4.567 is greater than 4.500.
Misinterpreting Repeating Decimals:
Repeating decimals can be tricky. For example, 0.333… (1/3) is often mistaken as being equal to 0.33. To compare accurately, consider enough digits to make a valid comparison. If comparing 0.333… and 0.33, recognize that 0.333… is slightly larger than 0.33.
Ignoring the Whole Number Part:
Always start by comparing the whole number parts of the decimals. If the whole number parts are different, the decimal with the larger whole number is greater, regardless of the decimal portion. For example, 5.1 is greater than 4.99, because 5 is greater than 4.
Examples of Common Mistakes:
- Mistake: Assuming 0.2 is greater than 0.25 because 2 is greater than 25.
  - Correction: Rewrite 0.2 as 0.20. Comparing 0.20 and 0.25, 0.25 is greater.
- Mistake: Thinking 0.07 is the same as 0.7.
  - Correction: Recognize that 0.07 is seven hundredths, while 0.7 is seven tenths. Therefore, 0.7 > 0.07.
- Mistake: Comparing 1.8 and 1.85 without aligning:
```
1.  8
2.  85  (Incorrect Alignment)
```
  - Correction: Align properly:
```
1.  80
2.  85
```
  Now it’s clear that 1.85 is greater than 1.80.

By being mindful of these common mistakes and practicing correct comparison techniques, you can improve your accuracy and confidence when working with decimals. For additional tips and practice exercises, visit COMPARE.EDU.VN, where we provide comprehensive resources for mastering decimal concepts.

8. Real-World Applications of Comparing Decimals

Comparing decimals is not just a mathematical exercise; it has numerous practical applications in everyday life. Understanding how to compare decimals accurately can help you make informed decisions in various situations.

Shopping and Finance:
- Price Comparison: When shopping, you often need to compare the prices of similar items. For example, comparing the price per unit of different sizes of a product involves comparing decimals. If a 1.5-liter bottle of juice costs $3.75 and a 2-liter bottle costs $4.80, you can calculate the price per liter to determine the better deal:
  - 1. 5-liter bottle: $3.75 ÷ 1.5 = $2.50 per liter
  - 2-liter bottle: $4.80 ÷ 2 = $2.40 per liter
  In this case, the 2-liter bottle is the better deal because it has a lower price per liter.
- Interest Rates: Comparing interest rates on loans or savings accounts involves comparing decimals. A higher interest rate on a savings account means more earnings, while a lower interest rate on a loan means less cost.
Cooking and Baking:
- Recipe Adjustments: When adjusting recipes, you often need to compare and measure decimal amounts of ingredients. For example, if a recipe calls for 0.75 cups of flour and you want to halve the recipe, you need to calculate half of 0.75, which is 0.375 cups.
- Nutritional Information: Comparing nutritional information on food labels involves comparing decimal values of calories, fat, protein, and other nutrients to make healthier choices.
Sports and Performance:
- Timing and Scores: In sports, decimals are used to measure time, distance, and scores. Comparing these decimals is essential for determining winners and tracking performance. For example, in a race, a time of 10.25 seconds is better than 10.3 seconds.
- Statistics: Athletes and coaches use statistics involving decimals to analyze performance and make improvements. For example, comparing batting averages (e.g., 0.325 vs. 0.280) helps evaluate a player’s hitting ability.
Science and Engineering:
- Measurements: Scientific and engineering measurements often involve decimals. Comparing these measurements is crucial for accuracy and precision. For example, comparing the diameters of two wires (e.g., 0.125 cm vs. 0.126 cm) can be important in electronics.
- Data Analysis: Scientists use decimals to analyze data and draw conclusions. Comparing decimal values in experiments helps in understanding trends and patterns.
Everyday Life Examples:
- Fuel Efficiency: Comparing the fuel efficiency of different cars involves comparing miles per gallon (MPG), which are often expressed as decimals.
- Temperature Readings: Comparing temperature readings in weather forecasts or when monitoring health involves comparing decimals.
Detailed Examples:
- Example 1: Choosing a Bank Account:
  - Bank A offers a savings account with an annual interest rate of 0.025 (2.5%).
  - Bank B offers a savings account with an annual interest rate of 0.0275 (2.75%).
  - Comparing 0.025 and 0.0275, Bank B offers a higher interest rate, making it the better choice.
- Example 2: Calculating Medication Dosage:
  - A doctor prescribes 0.15 grams of a medication.
  - The available tablets are 0.125 grams each.
  - To determine if one tablet is sufficient, compare 0.15 and 0.125. Since 0.15 > 0.125, one tablet is not enough; a portion of a second tablet is needed.
- Example 3: Comparing Travel Distances:
  - Route A is 12.45 miles long.
  - Route B is 12.38 miles long.
  - Comparing 12.45 and 12.38, Route B is shorter, making it the quicker option.

Understanding and applying decimal comparison skills can significantly improve your ability to make informed decisions in these and many other real-world scenarios. For more practical examples and resources, visit COMPARE.EDU.VN, where we provide comprehensive guides to help you master these essential skills.

9. Advanced Techniques: Comparing Decimals with Different Units

Comparing decimals becomes more complex when the numbers are in different units or formats. In such cases, it’s essential to convert the numbers to a common unit or format before making the comparison. This ensures an accurate and meaningful comparison.

Converting Units:
- Length: When comparing lengths in different units (e.g., meters and centimeters), convert them to the same unit. For example, compare 1.5 meters and 160 centimeters:
  - Convert 1.5 meters to centimeters: 1.5 m * 100 cm/m = 150 cm
  - Now compare 150 cm and 160 cm.
  - Since 160 cm > 150 cm, 160 centimeters is longer than 1.5 meters.
- Weight: Similarly, when comparing weights in different units (e.g., kilograms and grams), convert them to the same unit. For example, compare 2.2 kilograms and 2100 grams:
  - Convert 2.2 kilograms to grams: 2.2 kg * 1000 g/kg = 2200 g
  - Now compare 2200 g and 2100 g.
  - Since 2200 g > 2100 g, 2.2 kilograms is heavier than 2100 grams.
- Volume: When comparing volumes in different units (e.g., liters and milliliters), convert them to the same unit. For example, compare 0.75 liters and 700 milliliters:
  - Convert 0.75 liters to milliliters: 0.75 L * 1000 mL/L = 750 mL
  - Now compare 750 mL and 700 mL.
  - Since 750 mL > 700 mL, 0.75 liters is greater than 700 milliliters.
Converting Formats:
- Fractions and Decimals: As discussed earlier, convert fractions to decimals to compare them easily with other decimals. For example, compare 3/8 and 0.35:
  - Convert 3/8 to a decimal: 3 ÷ 8 = 0.375
  - Now compare 0.375 and 0.35.
  - Since 0.375 > 0.35, 3/8 is greater than 0.35.
- Percentages and Decimals: Convert percentages to decimals by dividing by 100. For example, compare 45% and 0.42:
  - Convert 45% to a decimal: 45 ÷ 100 = 0.45
  - Now compare 0.45 and 0.42.
  - Since 0.45 > 0.42, 45% is greater than 0.42.
Step-by-Step Examples:
- Example 1: Comparing Land Areas:
  - Plot A is 0.5 acres.
  - Plot B is 2000 square meters.
  - Convert acres to square meters (1 acre = 4046.86 square meters): 0.5 acres * 4046.86 m²/acre = 2023.43 m²
  - Now compare 2023.43 m² and 2000 m².
  - Since 2023.43 m² > 2000 m², Plot A is larger than Plot B.
- Example 2: Comparing Speeds:
  - Car A travels at 60 miles per hour.
  - Car B travels at 90 kilometers per hour.
  - Convert kilometers per hour to miles per hour (1 km/h = 0.621371 mph): 90 km/h * 0.621371 mph/km/h = 55.92 mph
  - Now compare 60 mph and 55.92 mph.
  - Since 60 mph > 55.92 mph, Car A is faster than Car B.
- Example 3: Comparing Recipe Ingredients:
  - Recipe A calls for 1.25 cups of sugar.
  - Recipe B calls for 300 milliliters of sugar.
  - Convert cups to milliliters (1 cup = 236.588 milliliters): 1.25 cups * 236.588 mL/cup = 295.74 mL
  - Now compare 295.74 mL and 300 mL.
  - Since 300 mL > 295.74 mL, Recipe B requires more sugar than Recipe A.

By mastering the techniques for converting units and formats, you can confidently compare decimals in a wide range of scenarios. For more advanced tips and resources, visit COMPARE.EDU.VN, where we provide comprehensive guides to help you excel in numerical comparisons.

10. Practice Problems to Sharpen Your Decimal Comparison Skills

To reinforce your understanding and enhance your skills in comparing decimals, here are several practice problems with detailed solutions. Working through these problems will help you become more confident and accurate in your comparisons.

Problem 1: Compare 0.45 and 0.405
- Solution:
  - Align the decimal points:
```
0.  450
1.  405
```
  - The tenths place is the same (4).
  - In the hundredths place, 5 is greater than 0.
  - Therefore, 0.45 > 0.405
Problem 2: Compare 1.6 and 1.58
- Solution:
  - Align the decimal points:
```
1.  60
2.  58
```
  - The whole number part is the same (1).
  - In the tenths place, 6 is greater than 5.
  - Therefore, 1.6 > 1.58
Problem 3: Compare 0.075 and 0.1
- Solution:
  - Align the decimal points:
```
0.  075
1.  100
```
  - In the tenths place, 1 is greater than 0.
  - Therefore, 0.1 > 0.075
Problem 4: Compare 2.35 and 2.349
- Solution:
  - Align the decimal points:
```
2.  350
3.  349
```
  - The whole number part is the same (2).
  - The tenths place is the same (3).
  - In the hundredths place, 5 is greater than 4.
  - Therefore, 2.35 > 2.349
Problem 5: Compare 5/8 and 0.6
- Solution:
  - Convert 5/8 to a decimal: 5 ÷ 8 = 0.625
  - Now compare 0.625 and 0.6
  - Align the decimal points:
```
0.  625
1.  600
```
  - In the hundredths place, 2 is greater than 0.
  - Therefore, 5/8 > 0.6
Problem 6: Compare 1.75 meters and 180 centimeters
- Solution:
  - Convert 1.75 meters to centimeters: 1.75 m * 100 cm/m = 175 cm
  - Now compare 175 cm and 180 cm
  - Since 180 cm > 175 cm, 180 centimeters is longer than 1.75 meters.
Problem 7: Arrange the following decimals in ascending order: 0.25, 0.3, 0.205, 0.35
- Solution:
  - Align the decimal points and add zeros as needed:
```
0.  250
1.  300
2.  205
3.  350
```
  - Comparing the tenths place, we see that 0.205 and 0.250 are smaller than 0.300 and 0.350.
  - Comparing 0.205 and 0.250, 0.205 is smaller.
  - Comparing 0.300 and 0.350, 0.300 is smaller.
  - Therefore, the ascending order is: 0.205, 0.25, 0.3, 0.35
Problem 8: A store offers two discounts: 20% off and 0.22 off the original price. Which discount is better?
- Solution:
  - Convert 20% to a decimal: 20 ÷ 100 = 0.2
  - Compare 0.2 and 0.22
  - Since 0.22 > 0.2, the 0.22 discount is better.

By working through these practice problems, you can solidify your understanding of decimal comparison and improve your problem-solving skills. For more practice problems and resources, visit COMPARE.EDU.VN, where we provide comprehensive tools to help you master numerical concepts.

Comparing decimals shares many similarities with comparing whole numbers, primarily relying on the understanding of place value. By aligning decimal points, comparing digits from left to right, and using zeros as placeholders, you can accurately determine the relative size of decimal numbers. Whether it’s for shopping, cooking, or scientific measurements, mastering decimal comparison is a valuable skill.

Ready to take your comparison skills to the next level? Visit compare.edu.vn for more detailed guides, interactive tools, and real-world examples. Make informed decisions with confidence, knowing you have the resources to compare any numbers accurately. Contact us at 333 Comparison Plaza, Choice City, CA 90210, United States, Whatsapp: +1 (626) 555-9090.

FAQ: Comparing Decimals

How do you compare decimals?

To compare decimals, align the decimal points and compare digits from left to right. Start with the whole number part, then move to the tenths