**WAEC Mathematics Four Figure Table PDF: See How To Use and Download.**

Contents

**Four Figure Table**: Hello Viewer, in this article i would like to discuss with you on how to use four figure table, Mathematics four figure table are lists of numbers showing the results of calculation with varying arguments. Before calculators were cheap and plentiful, people would use such tables to simplify and drastically speed up computation. Tables of logarithms and trigonometric functions were common in math and science textbooks. Specialized tables were published for applications such as astronomy, celestial navigation and statistics.

**How To Use Mathematics Four Figure Table to Find Logarithm and Antilog.**

**WAEC Four Figure Table: How to determine logarithm of a given number**

**How to determine the characteristic of a logx:**

**How to determine the mantissa of a logx:**

- Mantissa usually consist of a four digit number, and it comes after the decimal point.
- Mantissa is a non negative real number , which is less then 1.
- While determining the mantissa, the decimal point of the number has to be ignored.
- Most of the log tables give values of mantissa up to four digits only. For more than a four digit mantissa, we have to round off the last digit.
- Number with same sequence of digits have same mantissa.

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Example 1: Find the log of 500.2.Characteristic = 2.For mantissa, read from the table a number 5002. From the rows, choose 50, and read off from the number under the column 0. The number given in the log tables is 6990. Now read, in the same row, the mean difference under 2. This number is given as 2.Mantissa = 6990 + 2 = 6992.Thus log 500.2 = Characteristic of 500.2 + Mantissa of 500.2= 2 + 0.6992= 2.6992.

Example 2: Find the log of 72.98.Characteristic = 1.For mantissa, read from the table a number 7298. From the rows, choose 72, and read off from the number under the column 9. The number given in the log tables is 8627. Now read, in the same row, the mean difference under 8. This number is given as 5.Mantissa = 8627 + 5 = 8632.Thus log 72.98 = Characteristic of 72.98 + Mantissa of 72.98= 1 + 0.8632= 1.8632.

Example 3: Find the log of 0.0009887.Characteristic = -4.For mantissa, read from the table a number 9887. From the rows, choose 98, and read off from the number under the column 8. The number given in the log tables is 9948. Now read, in the same row, the mean difference under 7. This number is given as 3.Mantissa = 9948 + 3 = 9951.Thus log 0.0009887 = Characteristic of 0.0009887 + Mantissa of 0.0009887= – 4 + 0.9951= – 3.0049 ( The log of 0.009887 is also written as .9951, although its value is – 3.0049)

Example 4: Find the log of 0.1234.Characteristic = – 1.For mantissa, read from the table a number 1234. From the rows, choose 12, and read off from the number under the column 3. The number given in the log tables is 0899. Now read, in the same row, the mean difference under 4. This number is given as 14.Mantissa = 0899 + 14 = 0913.Thus log 0.1234 = Characteristic of 0.1234 + Mantissa of 0.1234= – 1 + 0. 0913= – 0.9087 or .0913.

**Mathematics Four Figure Table: Antilogarithm**

Remember that antiloga (x) = .

Example 1: Find the antilog of 2.6992.The number before the decimal point is 2, so the decimal point will be after the first 3 digits.From the antilog table, read off the row for .69 and column of 9; the number given in the table is 5000. The mean difference in the same row and under the column 2 is 2. To get the inverse of mantissa add 5000 + 2 = 5002.Now place a decimal point after the first 3 digits and you get the number 500.2Thus antilog 2.6992 = 500.2

Example 2: Find the antilog of – 1.9087Convert – 1.9087 in bar notation as follows :

characteristic of – 1.9087 = = –2

mantissa of –1.9087 = – 1.9087– (–2) = 0.0913

so –0.9087 = .0913

**NOTE:**The number before the decimal point is 0, the number of zeroes after the decimal point is one. From the antilog table, read off the row for .09 and column of 1; the number given in the table is 1233. The mean difference in the same row and under the column 3 is 1. To get the inverse of mantissa add 1233 + 1 = 1234. Now place a decimal point before the 1234 followed by a zero and you get the number 0.01234.

**Applications:**We will now see how logarithms and antilogarithms of numbers are useful for calculations which are complicated or have very large/small numbers.

Example 1: Find 80.92 * 19.45.Let x = 80.92 * 19.45Use the log function on both the sides.log x = log (80.92 * 19.45)log (80.92 * 19.45) = log 80.92 + log 19.45 ( from the laws of logarithms)From the log tables we get log 80.92 = 1.9080, log 19.45 = 1.2889Thus log (80.92 * 19.45) = 1.9080 + 1.2889 = 3.1969log x = 3.1969Now use antilog functions on both the sides.x = antilog 3.196From the antilog tables we see that the antilog of 3.1969 is 1573.0

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