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Chapter 4: Problem 46

Multiply. $$ \begin{array}{r} 16.34 \\ \times 0.000512 \\ \hline \end{array} $$

Short Answer

Expert verified
8.366080

Step by step solution

01

Remove Decimal Points

Convert the numbers to whole numbers by removing the decimal points. For 16.34, move the decimal point two places to the right to get 1634. For 0.000512, move the decimal point six places to the right to get 512,000.
02

Multiply the Whole Numbers

Multiply the whole numbers obtained from step 1. Multiply 1634 by 512,000.
03

Adjust the Decimal Point

Since the original decimal places in the factors were a total of eight (two in 16.34 and six in 0.000512), adjust the product by moving the decimal point eight places to the left.
04

Perform Final Multiplication and Adjustment

Calculate the intermediate product: 1634 multiplied by 512,000 equals 836,608,000. Adjust for the decimal places by moving the decimal point eight places to the left: 8.366080.

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Key Concepts

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

remove decimal points
To begin with decimal multiplication, the first step is to remove the decimal points from the numbers involved. This conversion simplifies the multiplication process. Let's break it down:
For the number 16.34, we move the decimal point two places to the right, converting it to 1634.
Similarly, for 0.000512, move the decimal point six places to the right, changing it to 512,000.
By removing the decimals, we make these numbers whole, which makes them easier to multiply.
adjust decimal point
After calculating the intermediate product, we need to account for the original decimal places. In our given numbers, 16.34 has 2 decimal places and 0.000512 has 6 decimal places, giving us a total of eight decimal places.
Once we have multiplied the whole numbers, we need to move the decimal point back to its proper position in the final product. This involves moving the decimal point eight places to the left in the result, ensuring the precision of the decimal operations is maintained.
intermediate product
After converting the decimals to whole numbers, the next step is to find the intermediate product. You do this by multiplying the whole numbers obtained after decimal removal.
In this exercise, multiply 1634 by 512,000:
1634 x 512,000 = 836,608,000.
This intermediate product is a crucial step that bridges the gap between initial decimal removal and final adjustment.
mathematical steps
The mathematical steps in decimal multiplication can be broken down into the following stages:
1. **Remove Decimal Points** - Turn the given decimals into whole numbers by shifting their decimal points.
2. **Multiply Whole Numbers** - Compute the product of the whole numbers.
3. **Adjust the Decimal Point** - Return the result to its appropriate decimal form by moving the decimal point back according to the original count of decimal places.
By following these steps methodically, you ensure accuracy and simplicity in handling decimal multiplication.

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Most popular questions from this chapter

Estimate. Indicate which of the choices is an appropriate estimate. \(78 \times 5.3\) a) 400 b) 800 c) 40 d) 8

Estimate by rounding as directed. $$ \begin{aligned} &12.9882-1.0115 ;\\\ &\text { nearest one } \end{aligned} $$

Estimate. Indicate which of the choices is an appropriate estimate. \(49 \times 7.89\) a) 400 b) 40 c) 4 d) 0.4

Add. $$ 65.987+9.4703+6744.02+1.0003+200.895 $$

Add. $$ 17+3.24+0.256+0.3689 $$
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