Problem 18 Multiply. $$7.2 \times 100$$... [FREE SOLUTION]

Chapter 5: Problem 18

Multiply. $$7.2 \times 100$$

Short Answer

Expert verified

7.2 multiplied by 100 equals 720.

Step by step solution

Understand the Problem

We need to multiply the number 7.2 by 100. This is a multiplication exercise that involves a decimal number and a whole number.

Position and Effect of 100 on Decimal Places

When multiplying a decimal by 100, you move the decimal point two places to the right. This is because 100 has two zeros, which corresponds to moving the decimal point two positions.

Perform the Multiplication

Starting with 7.2, move the decimal point two places to the right: The number 7.2 becomes 720 when the decimal moves past the 2 and then two more places.

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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 a fundamental concept in mathematics that helps us understand the value of each digit in a number. When you look at any number, each digit has its own place, and its value is determined by its position. For the number 7.2, we have two digits:

7 in the units place, representing 7 whole units.
2 in the tenths place, representing 0.2.

Knowing place value is essential for operations like multiplication, especially with decimals. It helps us maintain accuracy while moving or modifying digits during the calculation process. As multiplication affects place values, it鈥檚 crucial to keep track of each digit鈥檚 position. This will ensure that the result we get makes sense and retains the meaning of the original digits.

Decimal Point Movement

Moving the decimal point is a key operation when multiplying decimals by powers of 10, such as 100. This process simplifies calculations by essentially shifting numbers into larger or smaller units, depending on the direction. When you multiply by 100,

You shift the decimal point to the right.
You move the decimal point two places for 100 (since there are two zeros in 100).

For our problem, multiplying 7.2 by 100 involves moving the decimal two spots to the right, changing it from 7.2 to 720. This is because each shift to the right increases the digit鈥檚 place value by a power of ten, thus making the number larger. It is like saying you have 72 tens, instead of seven ones and two tenths.

Whole Numbers

Whole numbers are numbers without fractions or decimals. They include all positive numbers starting from 0. When working with whole numbers in multiplication, especially involving decimals, there's a more straightforward manipulation of the values. In our problem,

100 is a whole number.
It simplifies the multiplication as it aligns perfectly with the decimal shifting rule.

Multiplying a decimal by a whole number like 100 doesn鈥檛 require complex calculations, but rather an understanding of simple place value shifts. This makes the operation easy to compute: 7.2 transforms into a larger whole number, 720, after shifting the decimal place, highlighting the simplicity and power of using whole numbers in multiplication.

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91影视

Multiply. $$7.2 \times 100$$

Short Answer

Step by step solution

Understand the Problem

Position and Effect of 100 on Decimal Places

Perform the Multiplication

Key Concepts

Place Value

Decimal Point Movement

Whole Numbers

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