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Chapter 5: Problem 65

Round each decimal to the given place value. \(98,207.23,\) nearest ten

Short Answer

Expert verified
The number 98,207.23 rounded to the nearest ten is 98,210.

Step by step solution

01

Identify the Place Value

To round a number to the nearest ten, locate the tens place. In the number 98,207.23, the tens place is occupied by the digit 0 (in the '207' part).
02

Look at the Next Digit

Immediately to the right of the tens place is the ones place. The digit in the ones place is 7.
03

Apply the Rounding Rule

Since the digit in the ones place is 7, which is 5 or greater, round up the tens digit (0) by 1, changing it to 1.
04

Complete the Rounding

With the tens digit changing up from 0 to 1, the number 98,207 becomes 98,210. Any digits to the right of the tens place become 0.

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Key Concepts

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

Understanding Place Value
Place value is a fundamental concept in math that helps us understand the value of each digit in a number, depending on its position. Let's take the number 98,207.23 as an example.
  • The first digit, 9, represents ninety thousand because it is in the ten-thousands place.
  • The second digit, 8, represents eight thousand in the thousand place.
  • The third digit, 2, signifies two hundred in the hundreds place.
  • The fourth digit, 0, shows zero tens in the tens place.
  • The fifth digit, 7, indicates seven ones in the ones place.

Every digit has a specific value based on where it is located. Leftward, from right, each place value is 10 times the value of the place on its right. Understanding place values allows us to know which part of the number to focus on when rounding.
Applying Rounding Rules
Rounding numbers involves changing a number to one that is easier to work with, often based on certain rules. The most common rule for rounding is:
  • If the digit immediately to the right of your target place is 5 or greater, round up the target digit by one.
  • If that digit is less than 5, keep the target digit the same.
In our example of 98,207.23 and rounding to the nearest ten, the digit in the tens place is 0, and the digit in the ones place is 7. Because 7 is greater than 5, we round up 0 to 1. After rounding, all digits after the tens place become 0, transforming our number to 98,210. Rounding rules make it easier to simplify numbers quickly in everyday calculations.
Exploring Decimal Numbers
Decimal numbers contain a whole number part and a fractional part, divided by a decimal point. For instance, take the number 98,207.23.
The part before the decimal, 98,207, is the whole number, while the .23 is the decimal or fractional part. Decimal numbers allow precise representation of values less than one, which is essential in many real-world applications such as banking and measurement.
  • The first digit after the decimal - the tenths place, represents fractions of 10. In our example, 2 is in the tenths place or 2/10.
  • The following digit - the hundredths place, represents fractions of 100. Here, 3 is in the hundredths place or 3/100.
Understanding decimal numbers is crucial when rounding, especially if you need to round numbers that include these fractional parts. It helps prevent mistakes and ensures numbers are as precise as needed in calculations.

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Most popular questions from this chapter

Divide. Round the quotients as indicated. Divide: \(68.39 \div 0.6\). Round the quotient to the nearest tenth.

Multiply. $$0.5 \times 100$$

Write each decimal as a fraction or a mixed number. Write your answer in simplest form. $$ 11.406 $$

Divide. Divide 4.9 by -0.7 .

Write the numbers in order from smallest to largest. $$ \frac{5}{8}, 0.612,0.649 $$
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