Mathematics

Number

# Number notation and place value

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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**.