Problem 22 - Calculate With Confidence

Question

Express the following decimals to the nearest tenth. 1.75 _____

Step-by-Step Solution

Answer

1.8

Step 1: Identify the Hundredths Place

The number given is 1.75. To round to the nearest tenth, we need to look at the hundredths place. In 1.75, the number in the hundredths place is 5.

Step 2: Apply Rounding Rules

When the digit in the hundredths place is 5 or greater, we round the digit in the tenths place up by 1. In this case, the digit in the tenths place is 7. Since the digit in the hundredths place is 5, we will round up.

Step 3: Update the Tenths Place

Since the digit 5 in the hundredths place indicates that we round up, we increase the digit in the tenths place from 7 to 8. Therefore, 1.7 becomes 1.8 after rounding.

Key Concepts

Place Value

Understanding place value is crucial when working with decimals. Place value indicates the position of a digit in a number and determines its actual value. For example, in the number 1.75, place value helps us read and understand what each digit represents.

In a decimal, the place values to the right of the decimal point decrease by powers of ten:

• The first digit to the right is the tenths place, which means each unit is one-tenth or 0.1.
• The second digit to the right is the hundredths place, where each unit is one hundredth or 0.01.
• These positions help us decide how to round numbers appropriately based on which digit holds more value.

Recognizing place value is essential in accurately rounding decimals, because the value of each digit changes depending on its position in the number.

Tenths Place

The tenths place is the first position directly after the decimal point in a decimal number. It represents the number of tenths in the entire figure. In the number 1.75, the 7 is in the tenths place.

When rounding a decimal to the nearest tenth, this is the digit we want to adjust. The decision to keep it as is or increase it depends on the digit in the hundredths place. Here’s how it works:

• When the digit in the hundredths place (the next digit right) is less than 5, we keep the digit in the tenths place the same.
• If the digit in the hundredths place is 5 or greater, we round up the digit in the tenths place by 1.

This rounding process helps make the decimal number easier to work with, providing a simpler approximation.

Hundredths Place

In a decimal number, the hundredths place is two positions to the right of the decimal point. It tells us how many hundredths (or parts of 100) are in the number. For instance, in 1.75, the digit 5 is in the hundredths place.

The hundredths place plays a key role during rounding off decimal numbers. It determines whether the digit in the tenths place stays the same or increases. Here are some rounding rules involving the hundredths place:

• If the digit here is less than 5, the tenths place digit remains unchanged.
• When it is 5 or more, it signals us to round the tenths place digit one step up.

By using the digit in the hundredths place as a guide, rounding decimals becomes straightforward and consistent, improving precision in calculations.