Write each of the following numbers in standard form.
Problem 1 :
2.5 x 10^{2}
Problem 2 :
1.9 x 10^{-2}
Problem 3 :
5.236 x 10^{5}
Problem 4 :
6.415 x 10^{-6}
Problem 5 :
1.72 x 10^{9}
Problem 6 :
2.3 x 10^{-7}
Problem 7 :
3.6 x 10^{4}
Problem 8 :
2.05852 x 10^{5}
Problem 9 :
3.44909896 x 10^{6}
Problem 10 :
8.035 x 10^{-5}
Problem 11 :
A person can do 2.563 units of a certain work in a minute. Find the total number of units of the same work the person can do in 10^{3 }minutes.
Problem 12 :
A man walks 7.5 miles of distance in 10^{2} minutes. Find the speed of the man in miles per minute.
1. Answer :
2.5 x 10^{2}
Since the exponent of 10 is positive 2, the decimal point has to be shifted to the right by two digits.
In 2.5, there is only one digits to right of the decimal point.
So, we have to add one zero to move the decimal point to the right by two digits.
Therefore, the standard form of 2.5 x 10^{2} is
250
2. Answer :
1.9 x 10^{-2}
Since the exponent of 10 is negative 2, the decimal point has to be shifted to the left by two digits.
In 2.5, there is only one digits to left of the decimal point.
So, we have to add one zero to move the decimal point to the left by two digits.
Therefore, the standard form of 1.9 x 10^{-2} is
0.019
3. Answer :
5.236 x 10^{5}
Since the exponent of 10 is positive 5. the decimal point has to be shifted to the right by five digits
In 5.236, there are only three digits to right of the decimal point.
So, we have to add two zeros to move the decimal point to the right by five digits.
Therefore, the standard form of 5.236 x 10^{5} is
523600
4. Answer :
6.415 x 10^{-6}
Since the exponent of 10 is negative 6. the decimal has to be shifted to the left by six digits.
In 6.415, we have only 1 digit to the left of the decimal point.
So, we have to add five zeros to move the decimal point to the left by six digits.
Therefore, the standard form of 6.415 x 10^{-6} is
0.000006415
5. Answer :
1.72 x 10^{9}
Since the exponent of 10 is positive 9, the decimal point has to be shifted to the right by nine digits.
In 1.72, we have only two digits to the right of the decimal point.
So, we have to add seven zeros to move the decimal point to the right by nine digits.
Therefore, the standard form of 1.72 x 10^{9} is
1720000000
6. Answer :
2.3 x 10^{-7}
Since the exponent of 10 is negative 7, the decimal point has to be shifted to the left by seven digits.
In 2.3, we have only one digit to the left of the decimal point.
So, we have to add six zeros to move the decimal point to the left by seven digits.
Therefore, the standard form of 2.3 x 10^{-7} is
0.00000023
7. Answer :
3.6 x 10^{4}
Since the exponent of 10 is positive 4, the decimal point has to be shifted to the right by four digits.
In 3.6, we have only one digit to the right of the decimal point.
So, we have to add three zeros to move the decimal point to the right by four digits.
Therefore the standard form of 3.6 x 10^{4} is
36000
8. Answer :
2.05852 x 10^{5}
Since the exponent of 10 is positive 5, the decimal point has to be shifted to the right by five digits.
In 2.05852, we have five digits to the right of the decimal point.
So, we don't have to add zeros and we can move the decimal point to the right by five digits.
Therefore, the standard form of 2.05852 x 10^{5} is
205852
9. Answer :
3.44909896 x 10^{6}
Since the exponent of 10 is positive 6, the decimal point has to be shifted to the right by six digits.
In 3.44909896, we have eight digits to the right of the decimal point.
So, we don't have to add zeros and we can move the decimal point to the right by six digits.
Therefore, the standard form of 3.44909896 x 10^{6} is
3449098.96
10. Answer :
8.035 x 10^{-5}
Since the exponent of 10 is negative 5, the decimal point has to be shifted to the left by five digits.
In 8.035, we have only one digit to the left of the decimal point.
So, we have to add four zeros to move the decimal point to the left by five digits.
Therefore, the standard form of 8.035 x 10^{-5} is
0.00008035
11. Answer :
Number of units work completed in 1 minute :
= 2.563
Total number of units of the same work completed in 10^{3 }minutes.
= 2.563 x 10^{3}
Since the exponent of 10 is positive 3, the decimal point has to be shifted to the right by three digits.
In 2.563, we have three digits to the right of the decimal point.
So, we don't have to add zeros and we can move the decimal point to the right by three digits.
= 2563 units
12. Answer :
Formula for speed :
speed = distance ÷ time
Substitute distance = 7.5 and time = 10^{2}.
= 7.5 ÷ 10^{3}
= 7.5 x 10^{-3}
Since the exponent of 10 is negative 3, the decimal point has to be shifted to the left by three digits.
In 7.5, we have only one digit to the left of the decimal point.
So, we have to add two zeros to move the decimal point to the left by three digits.
= 0.0075 miles
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