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## McGraw-Hill Math Grade 7 Answer Key Lesson 16.3 Scientific Notation

**Exercises**

**CONVERT**

If the expression is in scientific notation, convert it to a number. If it is a number, convert it to scientific notation. Round all numbers to 6 places to the right of the decimal point when converting to scientific notation.

Question 1.

5 × 10^{5} = ____________

Answer:

5 × 10^{5} = **500,000**

Explanation:

The given expression is in scientific notation. To convert it into a number first we have to solve 10^{5}. Here base is 10 and exponent is 5. So, we have to multiply the base 10 by itself as five times the product is equal to 100,000. Multiply 5 with 100,000 the product is equal to 500,000.

Question 2.

478.23 = _____________

Answer:

478.23 = **4.7823 x 10 ^{2}**

Explanation:

There is a decimal point to the right of the given number. To convert the given number into scientific notation we have to move the decimal point to the left, one place value at a time and we have to count each time we move it.

We have to stop the process when the number is greater than 1 and less than 10. Here I moved two place values. So, the count is 10

^{2}. The number 478.23 in scientific notation as 4.7823 x 10

^{2}.

Question 3.

89,786 = _____________

Answer:

89,786 = **8.9786 x 10 ^{4}**

Explanation:

Imagine there is a decimal point to the right of the given number. To convert the given number into scientific notation we have to move the decimal point to the left, one place value at a time and we have to count each time we move it.

We have to stop the process when the number is greater than 1 and less than 10. Here I moved four place values. So, the count is 10

^{4}. The number 89,786 in scientific notation as 8.9786 x 10

^{4}.

Question 4.

6.721 × 10^{6} = ____________

Answer:

6.721 × 10^{6} = **6,721,000**

Explanation:

The given expression is in scientific notation. To convert it into a number first we have to solve 10^{6}. Here base is 10 and exponent is 6. So, we have to multiply the base 10 by itself as six times the product is equal to 1,000,000. Multiply 6.721 with 1,000,000 the product is equal to 6,721,000.

Question 5.

2.9731 × 10^{-2} = ______________

Answer:

2.9731 × 10^{-2} = **0.029731**

Explanation:

The given expression is in scientific notation. To convert it into a number first we have to solve 10^{-2}. Here base is 10 and exponent is -2. So, we have to multiply the base 10 by itself as two times the product is equal to 0.01. Multiply 2.9731 with 0.01 the product is equal to 0.029731.

Question 6.

691,273 = _____________

Answer:

691,273 = **6.91273 x 10 ^{5}**

Explanation:

Imagine there is a decimal point to the right of the given number. To convert the given number into scientific notation we have to move the decimal point to the left, one place value at a time and we have to count each time we move it.

We have to stop the process when the number is greater than 1 and less than 10. Here I moved five place values. So, the count is 10

^{5}. The number 691,273 in scientific notation as 6.91273 x 10

^{5}.

Question 7.

5,9178 × 10^{-3} = ____________

Answer:

5,9178 × 10^{-3} = **0.0059178**

Explanation:

The given expression is in scientific notation. To convert it into a number first we have to solve 10^{-3}. Here base is 10 and exponent is -3. So, we have to multiply the base 10 by itself as three times the product is equal to 0.001. Multiply 5,9178 with 0.001 the product is equal to 0.0059178.

Question 8.

8.72345 × 10^{10} = ______________

Answer:

8.72345 × 10^{10} = **87,234,500,000**

Explanation:

The given expression is in scientific notation. To convert it into a number first we have to solve 10^{10}. Here base is 10 and exponent is 10. So, we have to multiply the base 10 by itself as ten times. Multiply 8.72345 with 10^{10} the product is equal to 87,234,500,000.

Question 9.

6,664,475 = _____________

Answer:

6,664,475 = **6.664475 x 10 ^{6}**

Explanation:

Imagine there is a decimal point to the right of the given number. To convert the given number into scientific notation we have to move the decimal point to the left, one place value at a time and we have to count each time we move it.

We have to stop the process when the number is greater than 1 and less than 10. Here I moved six place values. So, the count is 10

^{6}. The number 6,664,475 in scientific notation as 6.664475 x 10

^{6}.

Question 10.

.0005123 = ______________

Answer:

.0005123= **5.123 x 10 ^{-4}**

Explanation:

There is a decimal point to the right of the given number. To convert the given number into scientific notation we have to move the decimal point to the right, one place value at a time and we have to count each time we move it.

We have to stop the process when the number is greater than 1 and less than 10. Here I moved four place values to left . So, the count is 10

^{-4}. The number .0005123 in scientific notation as 5.123 x 10

^{-4}.

Question 11.

8.9 = ______________

Answer:

8.9 = **8.9 x 10 ^{0}**

Explanation:

There is a decimal point to the right of the given number. The number 8 is greater than 1 and less than 10. Here I moved zero place values to right . So, the count is 10

^{0}. The number 8.9 in scientific notation as 8.9 x 10

^{0}.

Question 12.

100.235 = _______________

Answer:

100.235 = **1.00235 x 10 ^{2}**

Explanation:

There is a decimal point to the right of the given number. To convert the given number into scientific notation we have to move the decimal point to the left, one place value at a time and we have to count each time we move it.

We have to stop the process when the number is greater than 1 and less than 10. Here I moved two place values. So, the count is 10

^{2}. The number 100.235 in scientific notation as 1.00235 x 10

^{2}.

Question 13.

963,764 = _____________

Answer:

963,764 = **9.63764 x 10 ^{5}**

Explanation:

Imagine there is a decimal point to the right of the given number. To convert the given number into scientific notation we have to move the decimal point to the left, one place value at a time and we have to count each time we move it.

We have to stop the process when the number is greater than 1 and less than 10. Here I moved five place values. So, the count is 10

^{5}. The number 963,764 in scientific notation as 9.63764 x 10

^{5}.

Question 14.

4.6554 = _____________

Answer:

4.6554 = **4.6554** **x 10 ^{0}**

Explanation:

There is a decimal point to the right of the given number. The number 4 is greater than 1 and less than 10. Here I moved zero place values to right . So, the count is 10

^{0}. The number 4.6554 in scientific notation as 4.6554 x 10

^{0}.

Question 15.

789.23 = _______________

Answer:

789.23 = **7.8923 x 10 ^{2}**

Explanation:

There is a decimal point to the right of the given number. To convert the given number into scientific notation we have to move the decimal point to the left, one place value at a time and we have to count each time we move it.

We have to stop the process when the number is greater than 1 and less than 10. Here I moved two place values. So, the count is 10

^{2}. The number 789.23 in scientific notation as 7.8923 x 10

^{2}.

Question 16.

15,896,000,000,000 = ______________

Answer:

15,896,000,000,000 = **1.5896** **x 10 ^{13}**

Explanation:

Imagine there is a decimal point to the right of the given number. To convert the given number into scientific notation we have to move the decimal point to the left, one place value at a time and we have to count each time we move it.

We have to stop the process when the number is greater than 1 and less than 10. Here I moved thirteen place values. So, the count is 10

^{13}. The number 15,896,000,000,000 in scientific notation as 1.5896 x 10

^{13}.

Question 17.

8,999,345,000 = ________________

Answer:

8,999,345,000 = **8.999345 x 10 ^{9}**

Explanation:

Imagine there is a decimal point to the right of the given number. To convert the given number into scientific notation we have to move the decimal point to the left, one place value at a time and we have to count each time we move it.

We have to stop the process when the number is greater than 1 and less than 10. Here I moved nine place values. So, the count is 10

^{9}. The number 8,999,345,000 in scientific notation as 8.999345 x 10

^{9}.

Question 18.

1.697324 × 10^{4} = ______________

Answer:

1.697324 × 10^{4} = **16,973.24**

Explanation:

The given expression is in scientific notation. To convert it into a number first we have to solve 10^{4}. Here base is 10 and exponent is 4. So, we have to multiply the base 10 by itself as four times the product is equal to 10,000. Multiply 1.697324 with 10,000 the product is equal to 16,973.24.