| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 2.99 |
| Score | 0% | 60% |
Convert 0.0007636 to scientific notation.
| 0.764 x 10-3 | |
| 7.636 x 104 | |
| 7.636 x 105 | |
| 7.636 x 10-4 |
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:
0.0007636 in scientific notation is 7.636 x 10-4
A circular logo is enlarged to fit the lid of a jar. The new diameter is 50% larger than the original. By what percentage has the area of the logo increased?
| 15% | |
| 25% | |
| 30% | |
| 20% |
The area of a circle is given by the formula A = πr2 where r is the radius of the circle. The radius of a circle is its diameter divided by two so A = π(\( \frac{d}{2} \))2. If the diameter of the logo increases by 50% the radius (and, consequently, the total area) increases by \( \frac{50\text{%}}{2} \) = 25%
What is \( \frac{5}{4} \) - \( \frac{8}{10} \)?
| \(\frac{9}{20}\) | |
| 2 \( \frac{9}{20} \) | |
| 2 \( \frac{7}{20} \) | |
| 1 \( \frac{4}{20} \) |
To subtract these fractions, first find the lowest common multiple of their denominators. The first few multiples of 4 are [4, 8, 12, 16, 20, 24, 28, 32, 36, 40] and the first few multiples of 10 are [10, 20, 30, 40, 50, 60, 70, 80, 90]. The first few multiples they share are [20, 40, 60, 80] making 20 the smallest multiple 4 and 10 share.
Next, convert the fractions so each denominator equals the lowest common multiple:
\( \frac{5 x 5}{4 x 5} \) - \( \frac{8 x 2}{10 x 2} \)
\( \frac{25}{20} \) - \( \frac{16}{20} \)
Now, because the fractions share a common denominator, you can subtract them:
\( \frac{25 - 16}{20} \) = \( \frac{9}{20} \) = \(\frac{9}{20}\)
A menswear store is having a sale: "Buy one shirt at full price and get another shirt for 50% off." If Bob buys two shirts, each with a regular price of $43, how much will he pay for both shirts?
| $55.90 | |
| $21.50 | |
| $53.75 | |
| $64.50 |
By buying two shirts, Bob will save $43 x \( \frac{50}{100} \) = \( \frac{$43 x 50}{100} \) = \( \frac{$2150}{100} \) = $21.50 on the second shirt.
So, his total cost will be
$43.00 + ($43.00 - $21.50)
$43.00 + $21.50
$64.50
A triathlon course includes a 200m swim, a 50.4km bike ride, and a 13.3km run. What is the total length of the race course?
| 62.1km | |
| 55.4km | |
| 34.2km | |
| 63.9km |
To add these distances, they must share the same unit so first you need to first convert the swim distance from meters (m) to kilometers (km) before adding it to the bike and run distances which are already in km. To convert 200 meters to kilometers, divide the distance by 1000 to get 0.2km then add the remaining distances:
total distance = swim + bike + run
total distance = 0.2km + 50.4km + 13.3km
total distance = 63.9km