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Chapter 1: Problem 552

Round each number to the nearest hundredth. $$ 0.761 $$

Short Answer

Expert verified
0.76

Step by step solution

01

Identify the hundredth place

Locate the hundredth place in the given number 0.761. The hundredth place is the second digit to the right of the decimal point, which in this case is the digit 6.
02

Identify the thousandth place

Look at the digit immediately to the right of the hundredth place, which is in the thousandth place. In the number 0.761, the digit in the thousandth place is 1.
03

Apply rounding rules

According to the rounding rules, if the digit in the thousandth place is 5 or greater, increase the hundredth place digit by one. If it's less than 5, leave the hundredth place digit unchanged. Since the digit in the thousandth place (1) is less than 5, the hundredth place digit (6) remains 6.
04

Write the rounded number

After applying the rounding rules, the rounded number to the nearest hundredth is 0.76.

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Key Concepts

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

place value
Place value is an important concept in mathematics. It helps us understand the value of each digit in a number. In the number 0.761, its value depends on its place.
Each position to the right of the decimal point represents a fraction of 10. For instance:
- The first digit after the decimal is the tenths place.
- The second digit after the decimal is the hundredths place.
- The third digit after the decimal is the thousandths place.
Understanding place value is crucial for rounding numbers accurately, as it tells us which digit to look at and which to possibly change.
decimal numbers
Decimal numbers are numbers that contain a decimal point followed by digits that show a value less than one. In the example of 0.761, '0' is the whole number part and '.761' is the decimal part.
Decimal numbers are used to represent values that are more precise than whole numbers. Understanding how to read and write decimal numbers is essential for tasks in daily life including measuring, budgeting, and shopping.
Breaking down 0.761:
- 0 represents the whole number part.
- 7 represents seven-tenths (0.7).
- 6 represents six-hundredths (0.06).
- 1 represents one-thousandth (0.001).
rounding rules
Rounding rules help us simplify decimal numbers by shortening the number of digits after the decimal point. To round 0.761 to the nearest hundredth:
Step 1: Identify the hundredth place. This is the digit 6 in 0.761.
Step 2: Look at the thousandth place. This is the digit 1 in 0.761.
Remember the rounding rule:
  • If the digit in the thousandth place is 5 or greater, increase the hundredth place digit by one.
  • If the thousandth place digit is less than 5, leave the hundredth place digit unchanged.
Since the thousandth place digit is 1 (which is less than 5), the hundredth place digit remains 6.
Thus, 0.761 rounded to the nearest hundredth is 0.76.

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