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Chapter 6: Problem 40

Subtract 8.01629 from 9.00187 and round the result to three decimal places.

Short Answer

Expert verified
The result is 0.986.

Step by step solution

01

Align the Numbers

Write the numbers 9.00187 and 8.01629 in a column with their decimal points aligned. This will help ensure accuracy when performing the subtraction.
02

Perform the Subtraction

Subtract 8.01629 from 9.00187, starting from the rightmost digit and moving left. If necessary, borrow from the next column to complete the subtraction. The subtraction is: 9.00187 -8.01629 --------- 0.98558
03

Round the Result

Take the result, 0.98558, and round it to three decimal places. Look at the fourth decimal place; if it's 5 or more, increase the third decimal place by 1. Here, the fourth decimal place is 5, so round up. Therefore, the rounded result is 0.986.

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Key Concepts

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

Rounding Decimals
Rounding decimals is an essential skill, especially when you need to simplify a number to make it easier to interpret. At times, when a solution involves many decimal places, rounding helps in focusing on the most significant digits.
Here's a quick guide on how to round a decimal:
  • Identify the number of decimal places you are rounding to. In this case, it is three decimal places.
  • Look to the digit immediately to the right of your rounding place. This digit determines whether you round up or keep the number the same.
  • If the digit is 5 or more, you increase the rounding place by 1. If it's less than 5, you leave it as is.
In our original solution, we started with the number 0.98558. Looking at the fourth decimal place, which is 5, tells us to "round up" the third decimal place from 5 to 6. Hence, we arrived at 0.986.
Decimal Places
Decimal places indicate the digits following the decimal point in a number. They are crucial in determining the precision of your calculation.
Understanding decimal places is key for tasks like rounding or arithmetic operations like addition and subtraction. Here鈥檚 a breakdown:
  • The first digit after the decimal point is the tenths place.
  • The second is the hundredths place.
  • The third is the thousandths place, and so on.
More decimal places mean a more precise value, which can be necessary depending on the context. For the solution, we had five decimal places initially: 0.98558. This was key to performing an accurate subtraction operation, which was later rounded off to three decimal places for simplicity.
Borrowing in Subtraction
Borrowing is a method used in subtraction when a digit in the minuend (top number) is smaller than the corresponding digit in the subtrahend (bottom number). This is particularly critical when subtracting numbers with multiple decimal places.
To borrow in subtraction:
  • Check each column starting from the rightmost digit.
  • If a column's digit in the top number is smaller than in the bottom number, "borrow" from the column to the left. This means you decrease the left column's digit by one and add ten to the current column.
  • Continue across the number as needed, bringing down other unaffected digits.
For example, in subtracting 8.01629 from 9.00187, you may need to borrow to subtract certain digits. This ensures that subtraction is completed accurately, column by column, from right to left.

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Most popular questions from this chapter

Read each decimal by writing it in words. 4.0170

Round 0.0652 to the nearest hundredth.

Write each decimal using digits. Fifty-six and thirty-five ten-thousandths.

Perform each operation and simplify. $$ 0.014 \div 47.6 . \text { Round to three decimal places. } $$

Round each decimal to the specified position. 4.087 to the nearest hundredth.
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