Number Forms, Ratios, and Scientific Notation

Section 1Fractions, decimals, and percentages

A fraction shows part of a whole, a decimal uses place value, and a percentage means out of 100. In plain words, 3/4, 0.75, and 75% all describe the same amount. The thing to remember is that conversion is not a new topic - it is the same value wearing a different outfit.

Section 2Converting between forms

To change a fraction to a decimal, divide the numerator by the denominator. To change a decimal to a percentage, multiply by 100. To change a percentage to a decimal, divide by 100. Watch out: 0.08 is 8%, not 80%.

Section 3Percentage increase and decrease

A percentage increase adds a fraction of the original amount, while a percentage decrease subtracts it. For example, increasing J$2000 by 15% means finding 15% of 2000, then adding it. This is one of the most common exam slip-ups: students find the percentage amount but forget to add or subtract it.

Section 4Ratios and sharing

A ratio compares quantities in the same unit. If juice concentrate and water are mixed in the ratio 1:4, there is 1 part concentrate for every 4 parts water. Here's the trick: add the ratio parts first when a total is being shared.

Section 5Rates

A rate compares two quantities with different units, such as kilometres per hour, dollars per kilogram, or words per minute. Unit rate means the amount for one unit. For example, if 3 kg of rice costs J$900, the unit price is J$300 per kg.

Section 6Direct proportion

Two quantities are in direct proportion when they increase or decrease by the same factor. If 4 patties cost J$1200, then 8 patties cost twice as much, J$2400. Easy to mix up - direct proportion keeps the same multiplier, not the same difference.

Section 7Scientific notation

Scientific notation writes a number as a x 10^n, where a is at least 1 but less than 10. Large numbers use positive powers of 10, such as 560000 = 5.6 x 10^5. Small decimals use negative powers, such as 0.0042 = 4.2 x 10^-3.