➕ Algebra 1 · Exponents and Polynomials
Scientific Notation flashcards
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All 17 flashcards at a glance
Card 1
What does it mean for a number to be in scientific notation?
It is written as a × 10n with 1 ≤ a < 10 (one nonzero digit before the decimal point) and n an integer. All numbers in this lesson are positive.
Card 2
Write 52,000 in scientific notation.
5.2 × 104. Slide the point 4 places left.
Card 3
Write 0.0003 in scientific notation.
3 × 10−4. The point slides 4 places right, and the number is between 0 and 1.
Card 4
Write 8.04 × 103 in ordinary form.
8,040. Slide the point 3 places right.
Card 5
Write 1.9 × 10−2 in ordinary form.
0.019. Slide the point 2 places left.
Card 6
Why is the exponent negative for a number between 0 and 1?
Sliding the point right makes the front number 10 times bigger with each slide, so the power of 10 has to divide by 10 for each slide to keep the value the same: 10−1 = 1/10. The number itself stays positive.
Card 7
Is 0.58 × 107 in scientific notation? If not, fix it.
No, because 0.58 is less than 1. Slide the point one place right (0.58 → 5.8) and subtract 1 from the exponent: 5.8 × 106.
Card 8
Which is larger, 2.5 × 107 or 9.9 × 106?
2.5 × 107, which is 25,000,000 compared with 9,900,000. The bigger exponent wins, even though 9.9 is bigger than 2.5.
Card 9
Multiply (7 × 104)(8 × 102).
5.6 × 107. Fronts: 7 × 8 = 56. Exponents: 4 + 2 = 6. That is 56 × 106, and fixing the front number gives 5.6 × 107.
Card 10
Divide (9 × 105) ÷ (4 × 102).
2.25 × 103. Fronts: 9 ÷ 4 = 2.25. Exponents: 5 − 2 = 3. The front number is already between 1 and 10.
Card 11
Add 6 × 103 + 5 × 102.
6.5 × 103. Match the powers: 5 × 102 = 0.5 × 103. Then 6 + 0.5 = 6.5.
Card 12
A calculator shows 9.1E4. What number is that?
9.1 × 104 = 91,000. The E means “times ten to the power.” It is not the special number 2.718...
Card 13
In this lesson’s MOVE trick for converting to scientific notation, what do the letters stand for?
Move the decimal point until one nonzero digit is on its left. Observe how many places it moved (the size of the exponent). Verify the direction (left is positive, right is negative). Express the answer as the front number times the power of 10.
Card 14
In this lesson’s Match, Add, Fix trick for adding and subtracting, what are the three steps?
Match the powers of 10 (rewrite one number). Add or subtract the front numbers and keep the power. Fix the front number if it left the range from 1 up to (but not including) 10.
Card 15
Is the exponent in scientific notation the number of zeros?
No. It is the number of places the decimal point slides. 4,300,000 has five zeros, but it equals 4.3 × 106.
Card 16
How many times as large is 7 × 108 as 4 × 105?
Divide: (7 × 108) ÷ (4 × 105) = 1.75 × 103 = 1,750. It is 1,750 times as large.
Card 17
What happens to the exponents when you multiply two numbers in scientific notation? What about when you add two such numbers?
Multiplying: add the exponents. Adding: do not add them. Rewrite so the powers match, then add the front numbers and keep the power.