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Chapter 1: Problem 8

Round each of the numbers to the nearest ten. $$75$$

Short Answer

Expert verified
75 rounds to 80.

Step by step solution

01

Identify the Tens and Units Place

The number 75 has two digits, where 7 is in the tens place and 5 is in the units (or ones) place.
02

Evaluate the Units Digit

The units digit in the number 75 is 5. According to rounding rules, if the units digit is 5 or greater, we round up the tens digit to the next higher number.
03

Perform Rounding

Since the units digit (5) is exactly 5, we round up. We increase the tens digit (7) by 1, resulting in 8. Therefore, the rounded number becomes 80.

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Key Concepts

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

Tens Place
When we talk about the 'tens place,' it refers to the position of a digit in a number, specifically the second digit from the right. It represents how many groups of ten are in the number. For example, in the number 75, the 7 is in the tens place. This means there are 7 groups of ten, which is 70.
Understanding the tens place is important when rounding numbers because it helps us know which digit we are affecting when we round up or down.
To find the tens place, count from the right starting with zero. The first digit is the ones place, and the next digit is the tens place. In 75, zero is the ones place, and 1 is the tens place.
Units Place
The 'units place,' also known as the 'ones place,' is the first digit from the right in any whole number. This digit tells us how many single units are in a number.
For instance, in the number 75, the 5 is in the units place, signaling there are 5 single units.
Knowing the units place is significant in rounding since it helps decide whether to round up or stay the same. It is this digit that we evaluate according to the rounding rules.
Whenever we round numbers, especially to the nearest ten, we always look at this units place. A core reason is because any decision to either round up or not is based on this number.
  • If the units digit is 5 or more, like in 75, we round the tens place digit up.
  • If it is less than 5, we do nothing to the tens place and ignore the units digit by turning it into zero.
Rounding Rules
Rounding is a method for finding the nearest value at a specified level of precision. When dealing with whole numbers, rounding to the nearest ten is quite straightforward.
Here's how rounding works:
  • First, identify the tens place digit and the units place digit.
  • Look at the units digit. This digit tells us what to do next:
    • If the units digit is 5 or more, increase the tens digit by 1.
    • If it鈥檚 less than 5, keep the tens digit the same.
  • After determining what to do, change the units digit to zero.

Using the example of 75: since the units place is 5, the rule tells us to increase the tens place by 1, so 7 becomes 8. Then, replace the units digit with 0, turning 75 into 80.
Rounding according to these rules helps simplify numbers, which is especially useful in estimates and quick calculations. By mastering these rules, you can efficiently round numbers whenever needed!

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Most popular questions from this chapter

Add each of the following. (All problems involve carrying in at least one column. $$\begin{array}{r} 85 \\ 29 \\ \hline \end{array}$$

Write each of the following in symbols. a. The sum of 5 and 2 b. 3 added to 8

Find a solution for each equation. $$n+6=10$$

Write each of the following expressions in words. Use the word sum in each case. $$9+9$$

Divide. You shouldn't have any wrong answers because you can always check your results with multiplication. $$6 3 \div { 9 0 , 5 9 4 }$$
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