Fill In The Blanks To Complete The Table.$\[ \begin{tabular}{|l|l|} \hline $0.738 \times 1$ & $= \, $ \\ \hline $0.738 \times 10^1$ & $= \, $ \\ \hline $0.738 \times 10^2$ & $= \, $ \\ \hline $0.738 \times 10^3$ & $= \, $ \\ \hline $0.738 \times

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Understanding the Problem

In this problem, we are given a table with some missing values. The table involves multiplying a decimal number, 0.738, by powers of 10. Our task is to fill in the blanks and complete the table.

The Table

Expression Result
0.738×10.738 \times 1 $= , $
0.738×1010.738 \times 10^1 $= , $
0.738×1020.738 \times 10^2 $= , $
0.738×1030.738 \times 10^3 $= , $

Multiplying by Powers of 10

When we multiply a decimal number by a power of 10, we are essentially moving the decimal point of the number to the right by the number of places indicated by the exponent. For example, multiplying 0.738 by 10110^1 is equivalent to moving the decimal point one place to the right, resulting in 7.38.

Filling in the Blanks

Let's fill in the blanks in the table using this concept.

0.738×10.738 \times 1

When we multiply 0.738 by 1, the result is simply 0.738. This is because multiplying any number by 1 leaves the number unchanged.

0.738×1010.738 \times 10^1

As mentioned earlier, multiplying 0.738 by 10110^1 is equivalent to moving the decimal point one place to the right, resulting in 7.38.

0.738×1020.738 \times 10^2

Similarly, multiplying 0.738 by 10210^2 is equivalent to moving the decimal point two places to the right, resulting in 73.8.

0.738×1030.738 \times 10^3

Finally, multiplying 0.738 by 10310^3 is equivalent to moving the decimal point three places to the right, resulting in 738.

Completed Table

Expression Result
0.738×10.738 \times 1 =0.738= 0.738
0.738×1010.738 \times 10^1 =7.38= 7.38
0.738×1020.738 \times 10^2 =73.8= 73.8
0.738×1030.738 \times 10^3 =738= 738

Conclusion

In this problem, we filled in the blanks in the table by understanding the concept of multiplying decimal numbers by powers of 10. We saw that multiplying by a power of 10 is equivalent to moving the decimal point of the number to the right by the number of places indicated by the exponent. By applying this concept, we were able to complete the table with the correct results.

Key Takeaways

  • Multiplying a decimal number by a power of 10 is equivalent to moving the decimal point of the number to the right by the number of places indicated by the exponent.
  • The result of multiplying a decimal number by a power of 10 can be obtained by moving the decimal point of the number to the right by the number of places indicated by the exponent.
  • Understanding the concept of multiplying decimal numbers by powers of 10 is essential in solving problems involving exponential notation.

Practice Problems

  1. Fill in the blanks in the table:
Expression Result
0.456×10.456 \times 1 $= , $
0.456×1010.456 \times 10^1 $= , $
0.456×1020.456 \times 10^2 $= , $
0.456×1030.456 \times 10^3 $= , $

  1. Multiply 0.982 by 10410^4 and express the result in standard notation.

  2. Fill in the blanks in the table:

Expression Result
0.219×1010.219 \times 10^1 $= , $
0.219×1020.219 \times 10^2 $= , $
0.219×1030.219 \times 10^3 $= , $

Answer Key

1. Expression Result
0.456×10.456 \times 1 =0.456= 0.456
0.456×1010.456 \times 10^1 =4.56= 4.56
0.456×1020.456 \times 10^2 =45.6= 45.6
0.456×1030.456 \times 10^3 =456= 456
  1. 9820
  2. Expression Result
    0.219×1010.219 \times 10^1 =2.19= 2.19
    0.219×1020.219 \times 10^2 =21.9= 21.9
    0.219×1030.219 \times 10^3 =219= 219

Q: What is the concept of multiplying decimal numbers by powers of 10?

A: Multiplying a decimal number by a power of 10 is equivalent to moving the decimal point of the number to the right by the number of places indicated by the exponent.

Q: How do I fill in the blanks in a table involving multiplying decimal numbers by powers of 10?

A: To fill in the blanks, simply multiply the decimal number by the power of 10 indicated in the expression. For example, if the expression is 0.738×1020.738 \times 10^2, you would multiply 0.738 by 100 (which is 10210^2) to get 73.8.

Q: What is the result of multiplying a decimal number by a power of 10?

A: The result of multiplying a decimal number by a power of 10 is a number with the decimal point moved to the right by the number of places indicated by the exponent.

Q: How do I express the result of multiplying a decimal number by a power of 10 in standard notation?

A: To express the result in standard notation, simply move the decimal point of the original number to the right by the number of places indicated by the exponent.

Q: What is the difference between multiplying a decimal number by a power of 10 and multiplying it by a whole number?

A: When you multiply a decimal number by a whole number, you are simply multiplying the number by the whole number. However, when you multiply a decimal number by a power of 10, you are moving the decimal point of the number to the right by the number of places indicated by the exponent.

Q: Can I use this concept to multiply decimal numbers by negative powers of 10?

A: Yes, you can use this concept to multiply decimal numbers by negative powers of 10. When you multiply a decimal number by a negative power of 10, you are essentially moving the decimal point of the number to the left by the number of places indicated by the exponent.

Q: How do I fill in the blanks in a table involving multiplying decimal numbers by negative powers of 10?

A: To fill in the blanks, simply multiply the decimal number by the negative power of 10 indicated in the expression. For example, if the expression is 0.738×10−20.738 \times 10^{-2}, you would multiply 0.738 by 0.01 (which is 10−210^{-2}) to get 0.00738.

Q: What is the result of multiplying a decimal number by a negative power of 10?

A: The result of multiplying a decimal number by a negative power of 10 is a number with the decimal point moved to the left by the number of places indicated by the exponent.

Q: Can I use this concept to multiply decimal numbers by fractions?

A: Yes, you can use this concept to multiply decimal numbers by fractions. When you multiply a decimal number by a fraction, you are essentially multiplying the number by the numerator of the fraction and then dividing by the denominator.

Q: How do I fill in the blanks in a table involving multiplying decimal numbers by fractions?

A: To fill in the blanks, simply multiply the decimal number by the numerator of the fraction and then divide by the denominator. For example, if the expression is 0.738×1100.738 \times \frac{1}{10}, you would multiply 0.738 by 1 and then divide by 10 to get 0.0738.

Q: What is the result of multiplying a decimal number by a fraction?

A: The result of multiplying a decimal number by a fraction is a number that is the product of the decimal number and the numerator of the fraction, divided by the denominator of the fraction.

Conclusion

In this article, we have answered some frequently asked questions about multiplying decimal numbers by powers of 10 and fractions. We have seen that multiplying a decimal number by a power of 10 is equivalent to moving the decimal point of the number to the right by the number of places indicated by the exponent, and that multiplying a decimal number by a fraction is equivalent to multiplying the number by the numerator of the fraction and then dividing by the denominator. We hope that this article has been helpful in clarifying these concepts.