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Chapter 2: Problem 20

Multiply as indicated. 20\. } 1.2 \times 100

Short Answer

Expert verified
120

Step by step solution

01

- Understand the multiplication problem

Identify the numbers to be multiplied: 1.2 and 100.
02

- Convert to a simpler multiplication

Recognize that multiplying by 100 is the same as shifting the decimal point two places to the right.
03

- Perform the multiplication

Shift the decimal point in 1.2 two places to the right. This gives you 120.

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Key Concepts

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

Decimal Multiplication
Multiplying decimals might seem tricky, but with the right approach, it's quite manageable. When we multiply decimals, what we're really doing is multiplying two numbers without decimals first, and then placing the decimal in the correct position in the result.

Imagine multiplying 1.2 by 100 as if you're multiplying 12 by 1,000. This is easier because both numbers are whole numbers now. Once you get the product, which is 12,000, you'll place the decimal point back in the correct spot.

Essentially, the step-by-step number-crunching doesn't change much from standard whole number multiplication. The key difference lies in where the decimal point ends up at the end.
Shifting Decimal Points
An important trick to understand when multiplying by powers of 10 is the concept of 'shifting decimal points'.

For example, when you multiply a number by 10, you simply move the decimal one place to the right.

For 1.2:
  • 1.2 multiplied by 10 becomes 12.0 because the decimal point moves one place to the right.
  • 1.2 multiplied by 100, on the other hand, means moving the decimal two places to the right. So, 1.2 becomes 120.
Notice how this method simplifies the process!

Instead of multiplying through long methods, you just shift the decimal to quickly get the correct answer.
Basic Arithmetic Operations
It's important to recall that multiplying numbers, whether they're whole numbers or decimals, is one of the basic arithmetic operations.

Here's a quick recap:
  • When multiplying two numbers, the order doesn't matter (commutative property). So, 1.2 times 100 is the same as 100 times 1.2.
  • Multiplication of decimals follows the same rules as whole numbers, but with careful placement of the decimal point.
  • After multiplying, count the total number of decimal places in the factors to place the decimal correctly in the product.
By practicing these principles regularly, you'll gain a solid understanding and ease with all basic arithmetic operations, including multiplying decimals.

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