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Chapter 2: Problem 31

How much greater than 5.417 meters is 5.42 meters?

Short Answer

Expert verified
0.003 meters

Step by step solution

01

Identify the two numbers

Determine the two numbers involved in the exercise. The numbers are 5.417 meters and 5.42 meters.
02

Align the decimal points

To compare the two numbers easily, align the decimal points: 5.417 5.420
03

Subtract the smaller number from the larger number

Perform the subtraction: 5.420 - 5.417
04

Calculate the difference

Subtract the numbers: 5.420 - 5.417 = 0.003 meters

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

decimal places
When dealing with decimals, each digit after the decimal point represents a fraction of a whole number. The first digit is the tenths place, the second is the hundredths place, and the third is the thousandths place. For example, in the number 5.417, '4' is in the tenths place, '1' is in the hundredths place, and '7' is in the thousandths place. Recognizing these positions helps in performing accurate arithmetic operations such as addition, subtraction, multiplication, and division on decimal numbers.
number alignment
Aligning the numbers by their decimal points is crucial in decimal arithmetic. It ensures that digits in the same place value columns are subtracted from one another. Consider our exercise:
5.417
5.420
By aligning the decimal points, we clearly see that we compare hundredths with hundredths and thousandths with thousandths. If the numbers were not aligned correctly, this could lead to errors in calculation. Remember to add extra zeros if necessary to make the numbers have the same number of decimal places before performing arithmetic operations.
subtraction
Subtraction of decimal numbers follows the same basic principles as subtraction of whole numbers, but you need to be careful about the placement of the decimal point. In our exercise, we subtract 5.417 from 5.420.
Step-by-step, it looks like this:
  • Align the numbers: 5.420 - 5.417
  • Subtract the thousandths place: 0 - 7 (since this is less than zero, we need to borrow from the next place value)
  • Result series of subtractions leads to: 5.420 - 5.417 = 0.003
Pay careful attention to each place value during subtraction, and make sure the decimal points line up in your final answer.

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Most popular questions from this chapter

Tell the nearest tenths of a centimeter that each given measurement is between. For example, 3.66 is between 3.6 and 3.7 \(1.01 \mathrm{cm}\)

Find three fractions equivalent to each given fraction. \(\frac{12}{54}\)

Of the 560 students at Roosevelt Middle School, 240 participate in after- school sports. Of the 720 students at King Middle School, 300 participate in after-school sports. a. In which school does the greater number of students participate in sports? b. In which school does the greater fraction of students participate in sports?

\(\frac{132}{10,000}\)

Find a decimal equivalent for each fraction or mixed number. \(\frac{33}{24}\)
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