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Questions and Answers
What does the digit '7' represent in the decimal 45.678?
What does the digit '7' represent in the decimal 45.678?
How is the place value affected when moving from left to right across the decimal point?
How is the place value affected when moving from left to right across the decimal point?
In the decimal number 0.0093, which digit represents the hundredths place?
In the decimal number 0.0093, which digit represents the hundredths place?
What is the total number of decimal places in the product of 2.5 and 1.2?
What is the total number of decimal places in the product of 2.5 and 1.2?
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What would be the new value of 0.04 if it were multiplied by 100?
What would be the new value of 0.04 if it were multiplied by 100?
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In the decimal number 0.768, which digit contributes to the tenths place value?
In the decimal number 0.768, which digit contributes to the tenths place value?
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If a decimal number has three decimal places, what does that indicate about the placement of the decimal point in relation to whole numbers?
If a decimal number has three decimal places, what does that indicate about the placement of the decimal point in relation to whole numbers?
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For the decimal 2.045, which digit represents the thousands place?
For the decimal 2.045, which digit represents the thousands place?
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Study Notes
Multiplying Decimals
- Multiplication of decimals follows the same basic principles as multiplying whole numbers, but you need to account for the decimal points.
- To multiply decimals, first multiply the numbers as if they were whole numbers.
- Then, count the total number of decimal places in both the factors (the numbers being multiplied).
- Place the decimal point in the product (the result) so that it has the same number of decimal places.
Decimal Place Value
- Decimals represent fractional parts of a whole number.
- The value of each digit in a decimal depends on its position relative to the decimal point.
- Digits to the left of the decimal point represent whole numbers, while digits to the right represent fractional parts.
- The place value of each digit increases or decreases by a factor of 10 as you move from left to right or right to left from the decimal point.
- Each place value to the right of the decimal point represents a tenth, hundredth, thousandth, ten-thousandth, and so on.
- For example, in the decimal 3.14:
- The '3' represents 3 ones.
- The '1' represents 1 tenth.
- The '4' represents 4 hundredths.
Example
- Example: Multiply 2.5 x 1.2
- Multiply the numbers as if they were whole numbers: 25 x 12 = 300
- Count the decimal places in both factors: 2.5 has one decimal place, and 1.2 has one decimal place.
- The total number of decimal places is 1 + 1 = 2
- Place the decimal point in the product so that it has two decimal places: 3.00
- Thus: 2.5 x 1.2 = 3.00
- Alternatively, the result can be written as 3. (the trailing zeros are unnecessary in the decimal)
Strategies for Multiplying Decimals
- Estimating the product before multiplying can help in determining the reasonableness of the calculated solution.
- Multiplying decimals can be simplified by moving the decimal point; this often happens with powers of ten, resulting in a shift of the digits.
- Rounding the decimal factor(s) allows for a more straightforward calculation.
Multiplying by Powers of Ten
- When multiplying a decimal by a power of ten (10, 100, 1000, and so on), move the decimal point to the right by the number of zeros in the power of ten.
- Example: 0.56 × 10 = 5.6 (move the decimal point one place to the right)
- Example: 1.234 × 100 = 123.4 (move the decimal point two places to the right)
- Example: 0.678 × 1000 = 678 (move the decimal point three places to the right)
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Description
This quiz covers the principles of multiplying decimals, including how to account for decimal places. It also delves into the place value of decimals, illustrating the importance of each digit's position relative to the decimal point. Test your understanding of these concepts with this engaging quiz!
