Important formulas and concepts to remember for decimals in Grade 6

 Here are some important formulas and concepts to remember for decimals in Grade 6:

1. Basic Decimal Operations

• Addition/Subtraction of Decimals: Line up the decimal points and add or subtract as usual.
• Multiplication of Decimals: Multiply normally, then count and place the decimal point according to the total number of decimal places in both numbers.
• Division of Decimals: Move the decimal point in the divisor to make it a whole number, do the same shift in the dividend, then divide normally.

2. Converting Decimals

• Decimal to Fraction: Place the decimal over 10, 100, or 1000 depending on the number of decimal places, then simplify. $$0.75 = \frac{75}{100} = \frac{3}{4}$$
• Fraction to Decimal: Divide the numerator by the denominator. $$\frac{3}{4} = 3 \div 4 = 0.75$$
• Decimal to Percentage: Multiply by 100 and add %. $$0.75 \times 100 = 75\%$$
• Percentage to Decimal: Divide by 100. $$75\% = 75 \div 100 = 0.75$$

3. Rounding Decimals

• Look at the digit to the right of the place value you're rounding to:
  • If 5 or more, round up.
  • If less than 5, keep the digit the same.

4. Place Value Chart (up to thousandths)

Place	Thousands	Hundreds	Tens	Ones	.	Tenths	Hundredths	Thousandths
Example	1	2	3	4	.	5	6	7
Value	1000	200	30	4	.	0.5	0.06	0.007

5. Multiplying and Dividing by Powers of 10

• Multiplying by 10, 100, 1000: Move the decimal point right by the number of zeros. $$3.56 \times 100 = 356$$
• Dividing by 10, 100, 1000: Move the decimal point left by the number of zeros. $$356 \div 100 = 3.56$$

Here are the important formulas and concepts for Decimals in Grade 6:

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1. Basic Decimal Operations

• Addition/Subtraction of Decimals
  • Align the decimal points and add or subtract normally.
• Multiplication of Decimals
  • Multiply normally, then count and place the decimal point according to the total decimal places in both numbers.
  $$3.2 \times 1.5 = 4.80$$
• Division of Decimals
  • Move the decimal point in the divisor to make it a whole number, then do the same for the dividend and divide normally.
  $$4.2 \div 0.7 = 42 \div 7 = 6$$

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2. Converting Decimals

• Decimal to Fraction: Write the decimal over 10, 100, or 1000 based on decimal places and simplify. $$0.75 = \frac{75}{100} = \frac{3}{4}$$
• Fraction to Decimal: Divide numerator by denominator. $$\frac{3}{4} = 3 \div 4 = 0.75$$
• Decimal to Percentage: Multiply by 100 and add %. $$0.85 \times 100 = 85\%$$
• Percentage to Decimal: Divide by 100. $$65\% = 65 \div 100 = 0.65$$

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3. Rounding Decimals

• Look at the digit to the right of the place value being rounded:
  • If 5 or more, round up.
  • If less than 5, keep the digit the same.
  $$3.276 \approx 3.28 \text{ (Rounded to hundredths)}$$

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4. Place Value Chart (Up to Thousandths)

Place	Thousands	Hundreds	Tens	Ones	.	Tenths	Hundredths	Thousandths
Example	1	2	3	4	.	5	6	7
Value	1000	200	30	4	.	0.5	0.06	0.007

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5. Multiplying and Dividing by Powers of 10

• Multiplying by 10, 100, 1000: Move the decimal point right by the number of zeros. $$3.56 \times 100 = 356$$
• Dividing by 10, 100, 1000: Move the decimal point left by the number of zeros. $$356 \div 100 = 3.56$$

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