➕ Algebra 1 · Exponents and Polynomials
Scientific Notation: true or false
Decide fast, then read the reason. Wrong answers are the best teachers, so every statement explains itself.
All statements and answers
93,000,000 can be written as 9.3 × 107.
✓ True. Slide the point 7 places left to get 9.3. Check: 9.3 × 10,000,000 = 93,000,000.
0.0095 = 9.5 × 103.
✗ False. The point slides 3 places right to get 9.5, and the number is between 0 and 1, so the exponent is −3: 0.0095 = 9.5 × 10−3. The value 9.5 × 103 is 9,500.
27 × 103 is written in scientific notation.
✗ False. The front number must be less than 10, and 27 is not. Slide the point one place left and add 1 to the exponent: 27 × 103 = 2.7 × 104.
A negative exponent, as in 7 × 10−2, makes the number negative.
✗ False. A negative exponent means dividing by a power of 10, so it makes the number smaller, not negative. 7 × 10−2 = 7 ÷ 100 = 0.07, which is positive. Only a minus sign in front of the whole number would make it negative.
2.8 × 10−5 is greater than 2.8 × 10−6.
✓ True. The front numbers match, so compare exponents: −5 is greater than −6. In ordinary form, 0.000028 is greater than 0.0000028.
(2 × 103)(3 × 104) = 6 × 1012.
✗ False. When multiplying, add the exponents: 3 + 4 = 7. The product is 6 × 107. The exponent 12 comes from multiplying them.
(8 × 107) ÷ (2 × 103) = 4 × 104.
✓ True. Divide the front numbers: 8 ÷ 2 = 4. Subtract the exponents: 7 − 3 = 4.
6 × 107 + 2 × 106 = 8 × 107.
✗ False. The powers do not match, so you cannot add the front numbers yet. Rewrite 2 × 106 = 0.2 × 107 and add: 6.2 × 107. Check: 60,000,000 + 2,000,000 = 62,000,000.
On a calculator, 6E-4 stands for 6 × 10−4, which is 0.0006.
✓ True. The E means “times ten to the power.” Slide the point 4 places left: 0.0006.
5 × 100 = 5.
✓ True. Any nonzero base to the power 0 is 1, so 100 = 1 and 5 × 1 = 5.
When you multiply 6 × 104 by 5 × 102, the result 30 × 106 is already in scientific notation.
✗ False. The front number 30 is not less than 10. Slide the point one place left and add 1 to the exponent: 3 × 107.
In 4.8 × 10−7, the decimal point of 0.00000048 slid 7 places to the right.
✓ True. The point passes six zeros and the 4, so that is 7 slides to the right, which matches the exponent −7.
9 × 102 millimeters equals 9 × 10−1 meters.
✓ True. A millimeter is 10−3 meters, so 9 × 102 × 10−3 = 9 × 10−1 meters, which is 0.9 meters.