1.3 Standard Form and Significant Figures

• Standard Form expresses a number as a product of a number between 1 and 10 and a power of 10.
• To convert a number to Standard Form, you first identify the number between 1 and 10
• If the exponent in Standard Form is negative, you move the decimal point to the left
• Steps to convert numbers from standard form to decimal form

  1️⃣ Look at the exponent of 10

  2️⃣ If the exponent is positive, move the decimal point to the right

  3️⃣ If the exponent is negative, move the decimal point to the left
• 2.8 x 10^5 becomes 280,000 in decimal form

  True
• Leading zeros in a number are significant

  False
• Trailing zeros in a number with a decimal point are significant


  True
• What is another name for Standard Form?

  Scientific Notation
• What is one advantage of using Standard Form for calculations?

  Easy manipulation of powers
• How do you convert a number from Standard Form to Decimal Form if the exponent is positive?

  Move the decimal to the right
• -2.8 becomes 280,000 in decimal
• When converting 1.23 x 10^-3 to decimal form, you move the decimal point 3 places to the left
• All non-zero digits are always significant
• The number 0.0028 has 2 significant figures
• What is the significance of non-zero digits in significant figures?

  They are always significant
• When are trailing zeros significant in a number?

  With a decimal point
• Standard form expresses a number as a product of a number between 1 and 10 and a power of 10.


  True
• To convert a number to standard form, you must identify a number between 1 and 10.


  True
• If the exponent of 10 is positive, the decimal point is moved to the right
• Leading zeros are never significant.
• Zeros between non-zero digits are always significant


  True
• Exact values have an unlimited number of significant figures
• What is 123.4567 rounded to 3 significant figures?

  123
• Steps to multiply numbers in standard form

  1️⃣ Multiply the coefficients

  2️⃣ Add the powers of 10

  3️⃣ Round the result to the least number of significant figures

  4️⃣ Re-write in standard form if needed
• Maintaining accuracy requires rounding to the least number of significant figures

  True
• Zeros between non-zero digits are always significant
• The number 1200 has an ambiguous number of significant figures
• The general form of standard form is a number between 1 and 10 multiplied by a power of 10
• Steps to convert a number to standard form

  1️⃣ Identify the number between 1 and 10

  2️⃣ Count digits to the right of the first non-zero digit

  3️⃣ Write the number in the form: number x 10^power
• Significant figures include digits known with certainty plus the first uncertain digit.


  True
• Why do exact values have unlimited significant figures?

  They have no uncertainty
• Leading zeros are never significant
• If the digit to the right of the last significant figure is less than 5, round down


  True
• To add or subtract numbers in standard form, you must align the powers of 10

  True
• What is (3.45 x 10^5) / (6.78 x 10^4) rounded to 2 significant figures?

  5.1 x 10^0
• In Standard Form, the number between 1 and 10 is always multiplied by a power of 10.

  True
• Steps to convert a number to Standard Form

  1️⃣ Identify the number between 1 and 10

  2️⃣ Count digits to the right of the first non-zero digit

  3️⃣ Write the number in Standard Form
• To convert 2.8 x 10^5 to decimal form, you move the decimal point 5 places to the right.

  True
• If the exponent of 10 in standard form is positive, you move the decimal point to the right


  True
• What are significant figures?

  Digits contributing to accuracy