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Chapter 5: Problem 142

In the following exercises, multiply. $$(99.4)(1,000)$$

Short Answer

Expert verified
99.4 multiplied by 1,000 is 99,400.

Step by step solution

01

Understand the Problem

The goal is to multiply 99.4 by 1,000. We need to compute the product of these two numbers.
02

Use Basic Multiplication Rules

Recall that multiplying a number by 1,000 involves shifting the decimal point to the right by three places.
03

Perform the Multiplication

Take the number 99.4 and move the decimal point three places to the right: 99.4 -> 99400

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Key Concepts

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

Decimal Point
The decimal point is a dot used to separate the whole number part from the fractional part of a number. Understanding how to move the decimal point is key when performing multiplication, especially by powers of 10 such as 1,000. For example, starting with the number 99.4, the decimal point is immediately after the digit 9 in the ones place. When multiplying by 1,000, you shift the decimal point three places to the right. This operation changes the position of the digits, turning 99.4 into 99400.
Place Value
Place value helps us understand the value of each digit in a number based on its position. In the number 99.4, each digit has a specific place value: 9 in the tens place, 9 in the ones place, and 4 in the tenths place. When we move the decimal point three places to the right, it means the digits shift to higher place values. The 9 in the tens place moves to the ten thousands place, the 9 in the ones place moves to the thousands place, effectively becoming 99400. This shift is what happens when multiplying by 1,000, resulting in a much larger number.
Basic Multiplication Rules
Basic multiplication rules are fundamental for solving problems like this one. A key rule is that multiplying by a power of 10 (like 10, 100, or 1,000) simplifies to shifting the decimal point. For instance, multiplying 99.4 by 10 shifts the decimal one place to the right, making it 994. When multiplying by 1,000, we shift it three places. Understanding this rule helps us quickly and accurately solve problems without needing extensive calculations. Applying this rule, 99.4 multiplied by 1,000 shifts the decimal three places, resulting in the final product of 99400.

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