Forms & Expressions
Express 10-4 as a decimal and as a fraction.
0.0001 and
1/100000
Calculate 830 x 104
8, 300, 000
Is 0.82 x 106 written correctly in scientific notation? If not, why?
No, because the coefficient (0.82) is less than 1.
7.35 x 105
An auditorium has an area of 8.2 m2. Each square meter requires 10 x 10 tiles. How many tiles are needed in total? State your final answer using a therefore statement.
8.2 x (10 x 10) = 8.2 x 102 = 820
Therefore, 820 tiles are needed in total.
Write 10-3 as a fraction and in words.
0.001 and one thousandth
Calculate 4.9 x 10-3
0.0049
Is 45.1 x 10-3 written correctly in scientific notation? If not, explain why and rewrite it correctly.
No, because the coefficient (45.1) is greater than 1.
Written correctly in scientific notation: 4.51 x 10-2
Express 6.04 x 10-5 in standard form.
0.000 060 4
Company A earned $5.4 x 106 in profit. Company B earned $890,000. Who earned more money? Show your work and state your final answer using a therefore statement.
Company A: 5.4 x 106
Company B: 890,000 = 8.9 x 105
Compare powers of base 10.
106 > 105
Therefore Company A earned more money.
Express 0.000001 as a power of base 10 and in words.
10-6 and one millionth
Calculate
924.5 // 10^0
924.5
Is 6.02 x 100 written correctly in scientific notation? Explain why or why not.
Yes, because the coefficient (6.01) is greater than or equal to 1 and less than 10 and the exponent (0) is an integer.
Express 0.000 001 8 in scientific notation.
1.8 x 10-6
Mr. Pollock builds a deck with an area of 6.5 m2. Each square meter uses 10 x 10 wooden blocks. If each block costs 50 cents, how much will the blocks cost in total. Show your work. State your final answer using a therefore statement.
Total number of blocks needed = 6.5 x (10 x 10) = 6.5 x 102 = 650.
Total cost of blocks = 650 x 0.5 = 325
Therefore, the total cost of the blocks is $325.
Express 100, 000, 000 using exponential notation and in words
108 and one-hundred million
Determine the answer to the following question and state an equivalent multiplication expression.
350 // 10^-3
350, 000, 000 and 350 x 103
Identify and explain the error(s) in converting 0.00037 to scientific notation if a student wrote 37 x 105. Rewrite it correctly.
The exponent should be negative because the positive number in standard form is <1. Also the coefficient they wrote (37) is greater than 10.
Written correctly: 3.7 x 10-4
Which is larger, 6.1 x 104 or 290,000? Explain how you came to your answer.
Convert 290, 000 to scientific notation.
290, 000 = 2.9 x 105
Compare the two numbers in scientific notation.
6.1 x 104 and 2.9 x 105
The exponents are different, so we compare the powers of base 10.
104 < 105.
Therefore 290,000 is larger.
The distance from Earth to Saturn is approximately 1.4 x 109 km. The distance to Mars is approximately 2.25 x 108 km. How many kilometers farther is Saturn than Mars. Express your answer in scientific notation using a therefore statement.
14 x 108 - 2.25 x 108 = (14 - 2.25) x 108 = 11.75 x 108 = 1.175 x 109
Therefore Saturn is 1.175 x 109 km farther.
Express 10-7 as a decimal, in words and repeated multiplication.
0.000 000 1, ten-millionths,
1/10 xx 1/10 xx 1/10 xx 1/10 xx 1/10 xx 1/10 xx 1/10
Calculate
0.072 xx 10^5 // 10^-2
0.72 xx 10^5 = 7, 200
7,200 // 10^-2 = 720,000
Rewrite 0.0089 x 10-2 so its in proper scientific notation.
8.9 x 10-5
Order these numbers from smallest to largest. Explain how you came to your answer.
3.4 x 10-3 and 8.9 x 10-4 and 0.0021
Convert all numbers to scientific notation.
0.0021 = 2.1 x 10-3
Compare all numbers in scientific notation
3.4 x 10-3 and 8.9 x 10-4 and 2.1 x 10-3
First compare exponents. 10-4 < 10-3 so 8.9 x 10-4 is smallest.
Then compare coefficients of remaining numbers. 3.4 > 2.1 so 3.4 x 10-3 is largest.
Put in order
8.9 x 10-4, 0.0021, 3.4 x 10-3
DAILY DOUBLE: The volume of the Sun is approximately 1.41 x 1018 km3 and the volume of Uranus is approximately 6.83 x 1013 km3. How many times larger is the Sun than Uranus? Express your answer in scientific notation, rounding the coefficient to the hundredths and in standard form. Be sure to state your final answer using a therefore statement.
Therefore, the Sun is approximately 2.06 x 104 or 20,600x larger than Uranus.
(1.41 / 6.83) x 1018-13 ~0.20644 x 105 = 2.06 x 104 = 20, 600