| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.26 |
| Score | 0% | 65% |
Convert 5,853,000 to scientific notation.
| 5.853 x 107 | |
| 5.853 x 10-6 | |
| 5.853 x 105 | |
| 5.853 x 106 |
A number in scientific notation has the format 0.000 x 10exponent. To convert to scientific notation, move the decimal point to the right or the left until the number is a decimal between 1 and 10. The exponent of the 10 is the number of places you moved the decimal point and is positive if you moved the decimal point to the left and negative if you moved it to the right:
5,853,000 in scientific notation is 5.853 x 106
A factor is a positive __________ that divides evenly into a given number.
integer |
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fraction |
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improper fraction |
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mixed number |
A factor is a positive integer that divides evenly into a given number. For example, the factors of 8 are 1, 2, 4, and 8.
Which of the following is an improper fraction?
\({7 \over 5} \) |
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\(1 {2 \over 5} \) |
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\({a \over 5} \) |
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\({2 \over 5} \) |
A rational number (or fraction) is represented as a ratio between two integers, a and b, and has the form \({a \over b}\) where a is the numerator and b is the denominator. An improper fraction (\({5 \over 3} \)) has a numerator with a greater absolute value than the denominator and can be converted into a mixed number (\(1 {2 \over 3} \)) which has a whole number part and a fractional part.
A sports card collection contains football, baseball, and basketball cards. If the ratio of football to baseball cards is 5 to 2 and the ratio of baseball to basketball cards is 5 to 1, what is the ratio of football to basketball cards?
| 1:8 | |
| 25:2 | |
| 9:6 | |
| 3:6 |
The ratio of football cards to baseball cards is 5:2 and the ratio of baseball cards to basketball cards is 5:1. To solve this problem, we need the baseball card side of each ratio to be equal so we need to rewrite the ratios in terms of a common number of baseball cards. (Think of this like finding the common denominator when adding fractions.) The ratio of football to baseball cards can also be written as 25:10 and the ratio of baseball cards to basketball cards as 10:2. So, the ratio of football cards to basketball cards is football:baseball, baseball:basketball or 25:10, 10:2 which reduces to 25:2.
What is \( \frac{7}{2} \) + \( \frac{3}{10} \)?
| 2 \( \frac{1}{5} \) | |
| 2 \( \frac{4}{8} \) | |
| 1 \( \frac{3}{11} \) | |
| 3\(\frac{4}{5}\) |
To add these fractions, first find the lowest common multiple of their denominators. The first few multiples of 2 are [2, 4, 6, 8, 10, 12, 14, 16, 18, 20] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [10, 20, 30, 40, 50] making 10 the smallest multiple 2 and 10 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{7 x 5}{2 x 5} \) + \( \frac{3 x 1}{10 x 1} \)
\( \frac{35}{10} \) + \( \frac{3}{10} \)
Now, because the fractions share a common denominator, you can add them:
\( \frac{35 + 3}{10} \) = \( \frac{38}{10} \) = 3\(\frac{4}{5}\)