12 multiple-choice questions, progressively harder.
In the number 3.2×1063.2 \times 10^{6}3.2×106, what is the exponent?
Solution
Correct answer: B
The exponent is the small raised number on the 101010.
3.2×106 ⇒ exponent 63.2 \times 10^{6} \;\Rightarrow\; \text{exponent } 63.2×106⇒exponent 6
The coefficient is 3.23.23.2, and the power of ten is 10610^{6}106.
Which number is written in proper scientific notation?
Correct answer: C
Proper scientific notation needs a coefficient aaa with 1≤a<101 \le a < 101≤a<10, that is, exactly one nonzero digit before the decimal point.
1≤5.1<101 \le 5.1 < 101≤5.1<10
The coefficient 5.15.15.1 is in range. The others fail: 454545 and 121212 are too big, and 0.60.60.6 is less than 111.
Write 1,0001{,}0001,000 in scientific notation.
Correct answer: A
The coefficient is 111, and the decimal point moves 333 places left to go from after the last zero in 1,000.1{,}000.1,000. to just after the leading 111.
1,000=1×1031{,}000 = 1 \times 10^{3}1,000=1×103
That matches 103=100010^{3} = 1000103=1000.
Write 8.5×1038.5 \times 10^{3}8.5×103 as an ordinary number.
The exponent 333 is positive, so move the decimal point 333 places to the right, padding with zeros.
8.5×103=8,5008.5 \times 10^{3} = 8{,}5008.5×103=8,500
A positive exponent makes the number larger.
Write 6×1046 \times 10^{4}6×104 as an ordinary number.
The exponent 444 moves the decimal point 444 places right. Starting from 6.6.6. there are no digits after the point, so four zeros fill the places.
6×104=60,0006 \times 10^{4} = 60{,}0006×104=60,000
That matches 6×10,000=60,0006 \times 10{,}000 = 60{,}0006×10,000=60,000.
In the number 9×10−29 \times 10^{-2}9×10−2, what is the exponent?
The exponent is the raised number on the 101010, including its sign.
9×10−2 ⇒ exponent −29 \times 10^{-2} \;\Rightarrow\; \text{exponent } -29×10−2⇒exponent −2
The negative sign is part of the exponent; the coefficient is 999.
Write 20,00020{,}00020,000 in scientific notation.
The coefficient is 222 (one nonzero digit before the point), and the decimal point moves 444 places left, from after the last zero in 20,000.20{,}000.20,000. to just after the 222.
20,000=2×10420{,}000 = 2 \times 10^{4}20,000=2×104
The coefficient 202020 is not allowed, since it is 101010 or more.
Which number is NOT in proper scientific notation?
Correct answer: D
The coefficient must satisfy 1≤a<101 \le a < 101≤a<10. Check each one.
0.8<10.8 < 10.8<1
The coefficient 0.80.80.8 is less than 111, so 0.8×1050.8 \times 10^{5}0.8×105 is not proper. The other coefficients (4.04.04.0, 1.91.91.9, 7.37.37.3) all lie between 111 and 101010.
Write 9.2×1059.2 \times 10^{5}9.2×105 as an ordinary number.
The exponent 555 moves the decimal point 555 places to the right. After 9.29.29.2 there is one digit past the point, so four zeros fill the rest.
9.2×105=920,0009.2 \times 10^{5} = 920{,}0009.2×105=920,000
Write 0.0050.0050.005 in scientific notation.
The number is between 000 and 111, so the decimal point moves right and the exponent is negative. Slide the point to just after the 555: from 0.0050.0050.005 that is 333 places right.
0.005=5×10−30.005 = 5 \times 10^{-3}0.005=5×10−3
The coefficient is 555, and the exponent is −3-3−3.
Which equals 10−210^{-2}10−2?
A negative exponent gives the reciprocal of the matching positive power, and 102=10010^{2} = 100102=100.
10−2=1102=1100=0.0110^{-2} = \frac{1}{10^{2}} = \frac{1}{100} = 0.0110−2=1021=1001=0.01
The value is a small positive number, not negative.
Write 0.080.080.08 in scientific notation.
The number is below 111, so the point moves right for a negative exponent. Slide it to just after the 888: from 0.080.080.08 that is 222 places right.
0.08=8×10−20.08 = 8 \times 10^{-2}0.08=8×10−2
The coefficient is 888, and the exponent is −2-2−2.
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