Number notation and place value
Number Notation
- Standard form notation: used to express very large or very small numbers. A number in standard form is written as a x 10^n where 1 ≤ a < 10 and n is an integer.
- Decimal notation: most common number notation. Includes both integer part and fractional part separated by a decimal point.
- Fractions: used to represent a part of a whole. It comprises of a numerator (top number) and a denominator (bottom number). Numerator indicates the number of parts, while denominator indicates the total number of equal parts in a whole.
- Percentage notation: used to represent a number as a fraction of 100. It's symbolized by the '%' sign.
Place Value
- Units place: the rightmost place in a number.
- Tens place: to the left of the units place. Each move to the left multiplies the place value by 10.
- Hundreds place: to the left of the tens. Continuing the pattern, each move to the left multiplies the place value by 10.
- Decimal place values: includes tenths (one place after the decimal), hundredths (two places after the decimal) and so on.
- Naming large numbers: Beyond hundreds, we use names such as thousands, millions, billions and so on according to the place value. For example, in number 1,000,000, the 1 is in the "millions" place.
Important Points
- Understand how to convert between different number notations (standard form, decimals, fractions, and percentages).
- Rounding numbers according to different place value is crucial. For example, if rounding to the nearest tens, the value in the units place will decide the result.
- Comparing and ordering numbers will require a solid understanding of both number notation and place value. For example, you need to be able to determine which is larger: 0.25 or 25%.
- Be aware of common misconceptions such as the belief that 0.5 is bigger than 0.45 because 5 is larger than 45. Always consider place value when comparing numbers.
- Practice converting between different forms and being precise with place value to build speed and confidence.